Jared Kaplan | Johns Hopkins University (original) (raw)
Papers by Jared Kaplan
We provide dramatic evidence that 'Mellin space' is the natural home for correlation functions in... more We provide dramatic evidence that 'Mellin space' is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into 'left' and 'right' sub-correlators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursive structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to tree-level Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space S-Matrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep analogy with the properties of flat space scattering amplitudes in momentum space, which suggests that the Mellin amplitude may provide a holographic definition of the flat space S-Matrix.
We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensi... more We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| |v| < 1. We prove that every CFT with a scalar operator φ must contain infinite sequences of operators O τ, with twist approaching τ → 2∆ φ + 2n for each integer n as → ∞. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the φ × φ OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.
We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "l... more We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1-loop, and are conjectured to do so at all loop orders. The scattering amplitude for n particles in the sector with k negative helicity gluons is associated with a simple integral over the space of k planes in n dimensions, with the action of parity and cyclic symmetries manifest. The residues of the integrand compute a basis for the leading singularities. A given leading singularity is associated with a particular choice of integration contour, which we explicitly identify at tree level and 1-loop for all NMHV amplitudes as well as the 8 particle N 2 MHV amplitude. We also identify a number of 2-loop leading singularities for up to 8 particles. There are a large number of relations among residues which follow from the multi-variable generalization of Cauchy's theorem known as the "global residue theorem". These relations imply highly non-trivial identities guaranteeing the equivalence of many different representations of the same amplitude. They also enforce the cancellation of non-local poles as well as consistent infrared structure at loop level. Our conjecture connects the physics of scattering amplitudes to a particular subvariety in a Grassmannian; space-time locality is reflected in the topological properties of this space.
We provide necessary and sufficient conditions for a Conformal Field Theory to have a description... more We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative '1/N ' expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be wellapproximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program.
We study the effective field theory of inflation, i.e. the most general theory describing the flu... more We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g 00 and K µν , the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.
We study a 2+1 dimensional theory of bosons and fermions with an ω ∝ k 2 dispersion relation. The... more We study a 2+1 dimensional theory of bosons and fermions with an ω ∝ k 2 dispersion relation. The most general interactions consistent with specific symmetries impart fractional statistics to the fermions. Unlike examples involving Chern-Simons gauge theories, our statistical phases derive from the exchange of gapless propagating bosons with marginal interactions. Even though no gap exists, we show that the anyonic statistics are precisely defined. Symmetries combine with the vacuum structure to guarantee the non-renormalization of our anyonic phases. arXiv:1205.6816v1 [hep-th] 30 May 2012 1 Despite the absence of a gap, the anyonic phase is well-defined, as we show in section 3.1
The consistency relation for the 3-point function of the CMB is a very powerful observational sig... more The consistency relation for the 3-point function of the CMB is a very powerful observational signature which is believed to be true for every inflationary model in which there is only one dynamical degree of freedom. Its importance relies on the fact that deviations from it might be detected in next generation experiments, allowing us to rule out all single field inflationary models. After making more precise the already existing proof of the consistency relation, we use a recently developed effective field theory for inflationary perturbations to provide an alternative and very explicit proof valid at leading non trivial order in slow roll parameters.
The best-studied version of the RS1 model has all the Standard Model particles confined to the Te... more The best-studied version of the RS1 model has all the Standard Model particles confined to the TeV brane. However, recent variants have the Standard Model fermions and gauge bosons located in the bulk five-dimensional spacetime. We study the potential reach of the LHC in searching for the lightest KK partner of the graviton in the most promising such models in which the right-handed top is localized very near the TeV brane and the light fermions are localized near the Planck brane. We consider both detection and the establishment of the spin-2 nature of the resonance should it be found.
We examine the implications of the recent CDF measurement of the top-quark forward-backward asymm... more We examine the implications of the recent CDF measurement of the top-quark forward-backward asymmetry, focusing on a scenario with a new color octet vector boson at 1-3 TeV. We study several models, as well as a general effective field theory, and determine the parameter space which provides the best simultaneous fit to the CDF asymmetry, the Tevatron top pair production cross section, and the exclusion regions from LHC dijet resonance and contact interaction searches. Flavor constraints on these models are more subtle and less severe than the literature indicates. We find a large region of allowed parameter space at high axigluon mass and a smaller region at low mass; we match the latter to an SU (3) 1 × SU (3) 2 /SU (3) c coset model with a heavy vector-like fermion. Our scenario produces discoverable effects at the LHC with only 1 − 2 fb −1 of luminosity at √ s = 7 − 8 TeV. Lastly, we point out that a Tevatron measurement of the b-quark forward-backward asymmetry would be very helpful in characterizing the physics underlying the top-quark asymmetry.
We consider a comprehensive set of simplified models that contribute to final states with top and... more We consider a comprehensive set of simplified models that contribute to final states with top and bottom quarks at the LHC. These simplified models are used to create minimal search strategies that ensure optimal coverage of new heavy flavor physics involving the pair production of color octets and triplets. We provide a set of benchmarks that are representative of model space, which can be used by experimentalists to perform their own optimization of search strategies. For data sets larger than 1 fb −1 , same-sign dilepton and 3b search regions become very powerful. Expected sensitivities from existing and optimized searches are given.
TeV-mass dark matter charged under a new GeV-scale gauge force can explain electronic cosmicray a... more TeV-mass dark matter charged under a new GeV-scale gauge force can explain electronic cosmicray anomalies. We propose that the CoGeNT and DAMA direct detection experiments are observing scattering of light stable states -"GeV-Matter" -that are charged under this force and constitute a small fraction of the dark matter halo. Dark higgsinos in a supersymmetric dark sector are natural candidates for GeV-Matter that scatter off protons with a universal cross-section of 5 × 10 −38 cm 2 and can naturally be split by 10-30 keV so that their dominant interaction with protons is down-scattering. As an example, down-scattering of an O(5) GeV dark higgsino can simultaneously explain the spectra observed by both CoGeNT and DAMA. The event rates in these experiments correspond to a GeV-Matter abundance of 0.2 − 1% of the halo mass density.
Experiments designed to measure neutrino oscillations also provide major opportunities for discov... more Experiments designed to measure neutrino oscillations also provide major opportunities for discovering very weakly coupled states. In order to produce neutrinos, experiments such as LSND collide thousands of Coulombs of protons into fixed targets, while MINOS and MiniBooNE also focus and then dump beams of muons. The neutrino detectors beyond these beam dumps are therefore an excellent arena in which to look for long-lived pseudoscalars or for vector bosons that kinetically mix with the photon. We show that these experiments have significant sensitivity beyond previous beam dumps, and are able to partially close the gap between laboratory experiments and supernovae constraints on pseudoscalars. Future upgrades to the NuMI beamline and Project X will lead to even greater opportunities for discovery. We also discuss thin target experiments with muon beams, such as those available in COMPASS, and show that they constitute a powerful probe for leptophilic PNGBs.
We analyze a simple Split Supersymmetry scenario where fermion masses come from anomaly mediation... more We analyze a simple Split Supersymmetry scenario where fermion masses come from anomaly mediation, yielding m s ∼ 1000 TeV, m 3/2 ∼ 100 TeV, and m f ∼ 1 TeV. We consider non-thermal dark matter production in the presence of moduli, and we find that the decay chains of moduli → LSPs and moduli → gravitinos → LSPs generate dark matter more efficiently than perturbative freeze-out, allowing for a light, LHC visible spectrum. These decaying moduli can also weaken cosmological constraints on the axion decay constant. With squark masses of order 1000 TeV, LHC gluinos will decay millimeters from their primary vertices, resulting in a striking experimental signature, and the suppression of Flavor Changing Neutral Currents is almost sufficient to allow arbitrary mixing in squark mass matrices. 1
Many proposed solutions to the hierarchy problem rely on dimensional transmutation in asymptotica... more Many proposed solutions to the hierarchy problem rely on dimensional transmutation in asymptotically free gauge theories, and these theories often have dual descriptions in terms of a warped extra dimension. Gravitational calculations show that the confining phase transition in Randall-Sundrum models is first-order and parametrically slower than the rate expected in large-N gauge theories. This is dangerous because it leads to an empty universe problem. We argue that this rate suppression arises from approximate conformal symmetry. Though this empty universe problem cannot be solved by using the radion for low-scale inflation, we argue that if the radion potential is asymptotically free, another instanton for the RS phase transition can proceed as e −N 2 . We also discuss the existence of light magnetic monopoles (∼ 100 TeV) as a possible signature of such a phase transition.
We analyze a simple Split Supersymmetry scenario where fermion masses come from anomaly mediation... more We analyze a simple Split Supersymmetry scenario where fermion masses come from anomaly mediation, yielding m s ∼ 1000 TeV, m 3/2 ∼ 100 TeV, and m f ∼ 1 TeV. We consider non-thermal dark matter production in the presence of moduli, and we find that the decay chains of moduli → LSPs and moduli → gravitinos → LSPs generate dark matter more efficiently than perturbative freeze-out, allowing for a light, LHC visible spectrum. These decaying moduli can also weaken cosmological constraints on the axion decay constant. With squark masses of order 1000 TeV, LHC gluinos will decay millimeters from their primary vertices, resulting in a striking experimental signature, and the suppression of Flavor Changing Neutral Currents is almost sufficient to allow arbitrary mixing in squark mass matrices. 1
We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and th... more We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk S-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic function with simple poles on the real axis. This provides a powerful and suggestive handle on the locality vis-a-vis analyticity properties of the S-Matrix. We begin to explore analyticity by showing how the familiar poles and branch cuts of scattering amplitudes arise from the holographic description. For this purpose we compute examples of Mellin amplitudes corresponding to 1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime limit of conformal blocks, implicitly relating the S-Matrix program to the Bootstrap program for CFTs. We use this connection to show how the existence of small black holes in AdS leads to a universal prediction for the conformal block decomposition of the dual CFT.
The marvelous simplicity and remarkable hidden symmetries recently uncovered in (Super) Yang-Mill... more The marvelous simplicity and remarkable hidden symmetries recently uncovered in (Super) Yang-Mills and (Super)Gravity scattering amplitudes strongly suggests the existence of a "weak-weak" dual formulation of these theories where these structures are made more manifest at the expense of manifest locality. In this note we suggest that in four dimensions, this dual description lives in (2,2) signature and is naturally formulated in twistor space. We begin at tree-level, by recasting the momentum-space BCFW recursion relation in a completely on-shell form that begs to be transformed into twistor space. Our transformation is strongly inspired by Witten's twistor string theory, but differs in treating twistor and dual twistor variables on a more equal footing; a related transcription of the BCFW formula using only twistor space variables has been carried out independently by Mason and Skinner. Using both twistor and dual twistor variables, the three and four-point amplitudes are strikingly simple-for Yang-Mills theories they are "1" or "-1". The BCFW computation of higher-order amplitudes can be represented by a simple set of diagrammatic rules, concretely realizing Penrose's program of relating "twistor diagrams" to scattering amplitudes. More specifically, we give a precise definition of the twistor diagram formalism developed over the past few years by Andrew Hodges. The "Hodges diagram" representation of the BCFW rules allows us to compute amplitudes and study their remarkable properties in twistor space. For instance the diagrams for Yang-Mills theory are topologically disks and not trees, and reveal striking connections between amplitudes that are not manifest in momentum space. Twistor space also suggests a new representation of the amplitudes directly in momentum space, that is naturally determined by the Hodges diagrams. The BCFW rules and Hodges diagrams also enable a systematic twistorial formulation of gravity. All tree amplitudes can be combined into an "S-Matrix" scattering functional which is the natural holographic observable in asymptotically flat space; the BCFW formula turns into a simple quadratic equation for this "S-Matrix" in twistor space, providing a holographic description of N = 4 SYM and N = 8 Supergravity at tree level. We move on to initiate the exploration of loop amplitudes in (2, 2) signature and twistor space, beginning with a discussion of their IR behavior. We find that the natural pole prescriptions needed for transformation to twistor space make the amplitudes perfectly well-defined objects, free of IR divergences. Indeed in momentum space, the loop amplitudes so regulated vanish for generic momenta, and transformed to twistor space, are even simpler than their tree-level counterparts: the full 4-pt one-loop amplitudes in N = 4 SYM are simply equal to "1" or "0"! This further supports the idea that there exists a sharply defined object corresponding to the S-Matrix in (2,2) signature, computed by a dual theory naturally living in twistor space.
Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation... more Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing understanding of the structure of scattering amplitudes has however been pointing to the opposite conclusion. At tree level, the BCFW recursion relations that completely determine the S-matrix are valid not for scalar theories but for gauge theories and gravity, with gravitational amplitudes exhibiting the best UV behavior at infinite complex momentum. At 1-loop, amplitudes in N = 4 SYM only have scalar box integrals, and it was recently conjectured that the same property holds for N = 8 SUGRA, which plays an important role in the suspicion that this theory may be finite. In this paper we explore and extend the S-matrix paradigm, and suggest that N = 8 SUGRA has the simplest scattering amplitudes in four dimensions. Labeling external states by supercharge eigenstates-Grassmann coherent states-allows the amplitudes to be exposed as completely smooth objects, with the action of SUSY manifest. We show that under the natural supersymmetric extension of the BCFW deformation of momenta, all tree amplitudes in N = 4 SYM and N = 8 SUGRA vanish at infinite complex momentum, and can therefore be determined by recursion relations. An important difference between N = 8 SUGRA and N = 4 SYM is that the massless S-matrix is defined everywhere on moduli space, and is acted on by a non-linearly realized E 7(7) symmetry. We elucidate how non-linearly realized symmetries are reflected in the more familiar setting of pion scattering amplitudes, and go on to identify the action of E 7(7) on amplitudes in N = 8 SUGRA. Moving beyond tree level, we give a simple general discussion of the structure of 1-loop amplitudes in any QFT, in close parallel to recent work of Forde, showing that the coefficients of scalar "triangle" and "bubble" integrals are determined by the "pole at infinite momentum" of products of tree amplitudes appearing in cuts. In N = 4 SYM and N = 8 SUGRA, the on-shell superspace makes it easy to compute the multiplet sums that arise in these cuts by relating them to the best behaved tree amplitudes of highest spin, leading to a straightforward proof of the absence of triangles and bubbles at 1-loop. We also argue that rational terms are absent. This establishes that 1-loop amplitudes in N = 8 SUGRA only have scalar box integrals. We give an explicit expression for 1-loop amplitudes for both N =4 SYM and N = 8 SUGRA in terms of tree amplitudes that can be determined recursively. These amplitudes satisfy further relations in N = 8 SUGRA that are absent in N = 4 SYM. Since both tree and 1-loop amplitudes for maximally supersymmetric theories can be completely determined by their leading singularities, it is natural to conjecture that this property holds to all orders of perturbation theory. This is the nicest analytic structure amplitudes could possibly have, and if true, would directly imply the perturbative finiteness of N = 8 SUGRA. All these remarkable properties of scattering amplitudes call for an explanation in terms of a "weak-weak" dual formulation of QFT, a holographic dual of flat space.
The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of ... more The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams.
We show that suitably regulated multi-trace primary states in large N CFTs behave like 'in' and '... more We show that suitably regulated multi-trace primary states in large N CFTs behave like 'in' and 'out' scattering states in the flat-space limit of AdS. Their transition matrix elements approach the exact scattering amplitudes for the bulk theory, providing a natural CFT definition of the flat space S-Matrix. We study corrections resulting from the AdS curvature and particle propagation far from the center of AdS, and show that AdS simply provides an IR regulator that disappears in the flat space limit.
We provide dramatic evidence that 'Mellin space' is the natural home for correlation functions in... more We provide dramatic evidence that 'Mellin space' is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into 'left' and 'right' sub-correlators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursive structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to tree-level Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space S-Matrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep analogy with the properties of flat space scattering amplitudes in momentum space, which suggests that the Mellin amplitude may provide a holographic definition of the flat space S-Matrix.
We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensi... more We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| |v| < 1. We prove that every CFT with a scalar operator φ must contain infinite sequences of operators O τ, with twist approaching τ → 2∆ φ + 2n for each integer n as → ∞. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the φ × φ OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.
We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "l... more We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1-loop, and are conjectured to do so at all loop orders. The scattering amplitude for n particles in the sector with k negative helicity gluons is associated with a simple integral over the space of k planes in n dimensions, with the action of parity and cyclic symmetries manifest. The residues of the integrand compute a basis for the leading singularities. A given leading singularity is associated with a particular choice of integration contour, which we explicitly identify at tree level and 1-loop for all NMHV amplitudes as well as the 8 particle N 2 MHV amplitude. We also identify a number of 2-loop leading singularities for up to 8 particles. There are a large number of relations among residues which follow from the multi-variable generalization of Cauchy's theorem known as the "global residue theorem". These relations imply highly non-trivial identities guaranteeing the equivalence of many different representations of the same amplitude. They also enforce the cancellation of non-local poles as well as consistent infrared structure at loop level. Our conjecture connects the physics of scattering amplitudes to a particular subvariety in a Grassmannian; space-time locality is reflected in the topological properties of this space.
We provide necessary and sufficient conditions for a Conformal Field Theory to have a description... more We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative '1/N ' expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be wellapproximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program.
We study the effective field theory of inflation, i.e. the most general theory describing the flu... more We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g 00 and K µν , the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.
We study a 2+1 dimensional theory of bosons and fermions with an ω ∝ k 2 dispersion relation. The... more We study a 2+1 dimensional theory of bosons and fermions with an ω ∝ k 2 dispersion relation. The most general interactions consistent with specific symmetries impart fractional statistics to the fermions. Unlike examples involving Chern-Simons gauge theories, our statistical phases derive from the exchange of gapless propagating bosons with marginal interactions. Even though no gap exists, we show that the anyonic statistics are precisely defined. Symmetries combine with the vacuum structure to guarantee the non-renormalization of our anyonic phases. arXiv:1205.6816v1 [hep-th] 30 May 2012 1 Despite the absence of a gap, the anyonic phase is well-defined, as we show in section 3.1
The consistency relation for the 3-point function of the CMB is a very powerful observational sig... more The consistency relation for the 3-point function of the CMB is a very powerful observational signature which is believed to be true for every inflationary model in which there is only one dynamical degree of freedom. Its importance relies on the fact that deviations from it might be detected in next generation experiments, allowing us to rule out all single field inflationary models. After making more precise the already existing proof of the consistency relation, we use a recently developed effective field theory for inflationary perturbations to provide an alternative and very explicit proof valid at leading non trivial order in slow roll parameters.
The best-studied version of the RS1 model has all the Standard Model particles confined to the Te... more The best-studied version of the RS1 model has all the Standard Model particles confined to the TeV brane. However, recent variants have the Standard Model fermions and gauge bosons located in the bulk five-dimensional spacetime. We study the potential reach of the LHC in searching for the lightest KK partner of the graviton in the most promising such models in which the right-handed top is localized very near the TeV brane and the light fermions are localized near the Planck brane. We consider both detection and the establishment of the spin-2 nature of the resonance should it be found.
We examine the implications of the recent CDF measurement of the top-quark forward-backward asymm... more We examine the implications of the recent CDF measurement of the top-quark forward-backward asymmetry, focusing on a scenario with a new color octet vector boson at 1-3 TeV. We study several models, as well as a general effective field theory, and determine the parameter space which provides the best simultaneous fit to the CDF asymmetry, the Tevatron top pair production cross section, and the exclusion regions from LHC dijet resonance and contact interaction searches. Flavor constraints on these models are more subtle and less severe than the literature indicates. We find a large region of allowed parameter space at high axigluon mass and a smaller region at low mass; we match the latter to an SU (3) 1 × SU (3) 2 /SU (3) c coset model with a heavy vector-like fermion. Our scenario produces discoverable effects at the LHC with only 1 − 2 fb −1 of luminosity at √ s = 7 − 8 TeV. Lastly, we point out that a Tevatron measurement of the b-quark forward-backward asymmetry would be very helpful in characterizing the physics underlying the top-quark asymmetry.
We consider a comprehensive set of simplified models that contribute to final states with top and... more We consider a comprehensive set of simplified models that contribute to final states with top and bottom quarks at the LHC. These simplified models are used to create minimal search strategies that ensure optimal coverage of new heavy flavor physics involving the pair production of color octets and triplets. We provide a set of benchmarks that are representative of model space, which can be used by experimentalists to perform their own optimization of search strategies. For data sets larger than 1 fb −1 , same-sign dilepton and 3b search regions become very powerful. Expected sensitivities from existing and optimized searches are given.
TeV-mass dark matter charged under a new GeV-scale gauge force can explain electronic cosmicray a... more TeV-mass dark matter charged under a new GeV-scale gauge force can explain electronic cosmicray anomalies. We propose that the CoGeNT and DAMA direct detection experiments are observing scattering of light stable states -"GeV-Matter" -that are charged under this force and constitute a small fraction of the dark matter halo. Dark higgsinos in a supersymmetric dark sector are natural candidates for GeV-Matter that scatter off protons with a universal cross-section of 5 × 10 −38 cm 2 and can naturally be split by 10-30 keV so that their dominant interaction with protons is down-scattering. As an example, down-scattering of an O(5) GeV dark higgsino can simultaneously explain the spectra observed by both CoGeNT and DAMA. The event rates in these experiments correspond to a GeV-Matter abundance of 0.2 − 1% of the halo mass density.
Experiments designed to measure neutrino oscillations also provide major opportunities for discov... more Experiments designed to measure neutrino oscillations also provide major opportunities for discovering very weakly coupled states. In order to produce neutrinos, experiments such as LSND collide thousands of Coulombs of protons into fixed targets, while MINOS and MiniBooNE also focus and then dump beams of muons. The neutrino detectors beyond these beam dumps are therefore an excellent arena in which to look for long-lived pseudoscalars or for vector bosons that kinetically mix with the photon. We show that these experiments have significant sensitivity beyond previous beam dumps, and are able to partially close the gap between laboratory experiments and supernovae constraints on pseudoscalars. Future upgrades to the NuMI beamline and Project X will lead to even greater opportunities for discovery. We also discuss thin target experiments with muon beams, such as those available in COMPASS, and show that they constitute a powerful probe for leptophilic PNGBs.
We analyze a simple Split Supersymmetry scenario where fermion masses come from anomaly mediation... more We analyze a simple Split Supersymmetry scenario where fermion masses come from anomaly mediation, yielding m s ∼ 1000 TeV, m 3/2 ∼ 100 TeV, and m f ∼ 1 TeV. We consider non-thermal dark matter production in the presence of moduli, and we find that the decay chains of moduli → LSPs and moduli → gravitinos → LSPs generate dark matter more efficiently than perturbative freeze-out, allowing for a light, LHC visible spectrum. These decaying moduli can also weaken cosmological constraints on the axion decay constant. With squark masses of order 1000 TeV, LHC gluinos will decay millimeters from their primary vertices, resulting in a striking experimental signature, and the suppression of Flavor Changing Neutral Currents is almost sufficient to allow arbitrary mixing in squark mass matrices. 1
Many proposed solutions to the hierarchy problem rely on dimensional transmutation in asymptotica... more Many proposed solutions to the hierarchy problem rely on dimensional transmutation in asymptotically free gauge theories, and these theories often have dual descriptions in terms of a warped extra dimension. Gravitational calculations show that the confining phase transition in Randall-Sundrum models is first-order and parametrically slower than the rate expected in large-N gauge theories. This is dangerous because it leads to an empty universe problem. We argue that this rate suppression arises from approximate conformal symmetry. Though this empty universe problem cannot be solved by using the radion for low-scale inflation, we argue that if the radion potential is asymptotically free, another instanton for the RS phase transition can proceed as e −N 2 . We also discuss the existence of light magnetic monopoles (∼ 100 TeV) as a possible signature of such a phase transition.
We analyze a simple Split Supersymmetry scenario where fermion masses come from anomaly mediation... more We analyze a simple Split Supersymmetry scenario where fermion masses come from anomaly mediation, yielding m s ∼ 1000 TeV, m 3/2 ∼ 100 TeV, and m f ∼ 1 TeV. We consider non-thermal dark matter production in the presence of moduli, and we find that the decay chains of moduli → LSPs and moduli → gravitinos → LSPs generate dark matter more efficiently than perturbative freeze-out, allowing for a light, LHC visible spectrum. These decaying moduli can also weaken cosmological constraints on the axion decay constant. With squark masses of order 1000 TeV, LHC gluinos will decay millimeters from their primary vertices, resulting in a striking experimental signature, and the suppression of Flavor Changing Neutral Currents is almost sufficient to allow arbitrary mixing in squark mass matrices. 1
We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and th... more We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk S-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic function with simple poles on the real axis. This provides a powerful and suggestive handle on the locality vis-a-vis analyticity properties of the S-Matrix. We begin to explore analyticity by showing how the familiar poles and branch cuts of scattering amplitudes arise from the holographic description. For this purpose we compute examples of Mellin amplitudes corresponding to 1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime limit of conformal blocks, implicitly relating the S-Matrix program to the Bootstrap program for CFTs. We use this connection to show how the existence of small black holes in AdS leads to a universal prediction for the conformal block decomposition of the dual CFT.
The marvelous simplicity and remarkable hidden symmetries recently uncovered in (Super) Yang-Mill... more The marvelous simplicity and remarkable hidden symmetries recently uncovered in (Super) Yang-Mills and (Super)Gravity scattering amplitudes strongly suggests the existence of a "weak-weak" dual formulation of these theories where these structures are made more manifest at the expense of manifest locality. In this note we suggest that in four dimensions, this dual description lives in (2,2) signature and is naturally formulated in twistor space. We begin at tree-level, by recasting the momentum-space BCFW recursion relation in a completely on-shell form that begs to be transformed into twistor space. Our transformation is strongly inspired by Witten's twistor string theory, but differs in treating twistor and dual twistor variables on a more equal footing; a related transcription of the BCFW formula using only twistor space variables has been carried out independently by Mason and Skinner. Using both twistor and dual twistor variables, the three and four-point amplitudes are strikingly simple-for Yang-Mills theories they are "1" or "-1". The BCFW computation of higher-order amplitudes can be represented by a simple set of diagrammatic rules, concretely realizing Penrose's program of relating "twistor diagrams" to scattering amplitudes. More specifically, we give a precise definition of the twistor diagram formalism developed over the past few years by Andrew Hodges. The "Hodges diagram" representation of the BCFW rules allows us to compute amplitudes and study their remarkable properties in twistor space. For instance the diagrams for Yang-Mills theory are topologically disks and not trees, and reveal striking connections between amplitudes that are not manifest in momentum space. Twistor space also suggests a new representation of the amplitudes directly in momentum space, that is naturally determined by the Hodges diagrams. The BCFW rules and Hodges diagrams also enable a systematic twistorial formulation of gravity. All tree amplitudes can be combined into an "S-Matrix" scattering functional which is the natural holographic observable in asymptotically flat space; the BCFW formula turns into a simple quadratic equation for this "S-Matrix" in twistor space, providing a holographic description of N = 4 SYM and N = 8 Supergravity at tree level. We move on to initiate the exploration of loop amplitudes in (2, 2) signature and twistor space, beginning with a discussion of their IR behavior. We find that the natural pole prescriptions needed for transformation to twistor space make the amplitudes perfectly well-defined objects, free of IR divergences. Indeed in momentum space, the loop amplitudes so regulated vanish for generic momenta, and transformed to twistor space, are even simpler than their tree-level counterparts: the full 4-pt one-loop amplitudes in N = 4 SYM are simply equal to "1" or "0"! This further supports the idea that there exists a sharply defined object corresponding to the S-Matrix in (2,2) signature, computed by a dual theory naturally living in twistor space.
Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation... more Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing understanding of the structure of scattering amplitudes has however been pointing to the opposite conclusion. At tree level, the BCFW recursion relations that completely determine the S-matrix are valid not for scalar theories but for gauge theories and gravity, with gravitational amplitudes exhibiting the best UV behavior at infinite complex momentum. At 1-loop, amplitudes in N = 4 SYM only have scalar box integrals, and it was recently conjectured that the same property holds for N = 8 SUGRA, which plays an important role in the suspicion that this theory may be finite. In this paper we explore and extend the S-matrix paradigm, and suggest that N = 8 SUGRA has the simplest scattering amplitudes in four dimensions. Labeling external states by supercharge eigenstates-Grassmann coherent states-allows the amplitudes to be exposed as completely smooth objects, with the action of SUSY manifest. We show that under the natural supersymmetric extension of the BCFW deformation of momenta, all tree amplitudes in N = 4 SYM and N = 8 SUGRA vanish at infinite complex momentum, and can therefore be determined by recursion relations. An important difference between N = 8 SUGRA and N = 4 SYM is that the massless S-matrix is defined everywhere on moduli space, and is acted on by a non-linearly realized E 7(7) symmetry. We elucidate how non-linearly realized symmetries are reflected in the more familiar setting of pion scattering amplitudes, and go on to identify the action of E 7(7) on amplitudes in N = 8 SUGRA. Moving beyond tree level, we give a simple general discussion of the structure of 1-loop amplitudes in any QFT, in close parallel to recent work of Forde, showing that the coefficients of scalar "triangle" and "bubble" integrals are determined by the "pole at infinite momentum" of products of tree amplitudes appearing in cuts. In N = 4 SYM and N = 8 SUGRA, the on-shell superspace makes it easy to compute the multiplet sums that arise in these cuts by relating them to the best behaved tree amplitudes of highest spin, leading to a straightforward proof of the absence of triangles and bubbles at 1-loop. We also argue that rational terms are absent. This establishes that 1-loop amplitudes in N = 8 SUGRA only have scalar box integrals. We give an explicit expression for 1-loop amplitudes for both N =4 SYM and N = 8 SUGRA in terms of tree amplitudes that can be determined recursively. These amplitudes satisfy further relations in N = 8 SUGRA that are absent in N = 4 SYM. Since both tree and 1-loop amplitudes for maximally supersymmetric theories can be completely determined by their leading singularities, it is natural to conjecture that this property holds to all orders of perturbation theory. This is the nicest analytic structure amplitudes could possibly have, and if true, would directly imply the perturbative finiteness of N = 8 SUGRA. All these remarkable properties of scattering amplitudes call for an explanation in terms of a "weak-weak" dual formulation of QFT, a holographic dual of flat space.
The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of ... more The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams.
We show that suitably regulated multi-trace primary states in large N CFTs behave like 'in' and '... more We show that suitably regulated multi-trace primary states in large N CFTs behave like 'in' and 'out' scattering states in the flat-space limit of AdS. Their transition matrix elements approach the exact scattering amplitudes for the bulk theory, providing a natural CFT definition of the flat space S-Matrix. We study corrections resulting from the AdS curvature and particle propagation far from the center of AdS, and show that AdS simply provides an IR regulator that disappears in the flat space limit.