On amplitudes in the self-dual sector of Yang-Mills theory (original) (raw)

Amplitudes in pure Yang-Mills and MHV Diagrams

Journal of High Energy Physics, 2007

We show how to calculate the one-loop scattering amplitude with all gluons of negative helicity in non-supersymmetric Yang-Mills theory using MHV diagrams. We argue that the amplitude with all positive helicity gluons arises from a Jacobian which occurs when one performs a Bäcklund-type holomorphic change of variables in the lightcone Yang-Mills Lagrangian. This also results in contributions to scattering amplitudes from violations of the equivalence theorem. Furthermore, we discuss how the one-loop amplitudes with a single positive or negative helicity gluon arise in this formalism. Perturbation theory in the new variables leads to a hybrid of MHV diagrams and lightcone Yang-Mills theory.

Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills

Journal of High Energy Physics, 2021

We present the inverse Penrose transform (the map from spacetime to twistor space) for self-dual Yang-Mills (SDYM) and its higher-spin extensions on a flat background. The twistor action for the higher-spin extension of SDYM (HS-SDYM) is of mathcalBF\mathcal{BF}mathcalBF BF -type. By considering a deformation away from the self-dual sector of HS-SDYM, we discover a new action that describes a higher-spin extension of Yang-Mills theory (HS-YM). The twistor action for HS-YM is a straightforward generalization of the Yang-Mills one.

One-loop maximal helicity violating amplitudes in N= 4 super Yang-Mills theories

Journal of High Energy Physics, 2004

One-loop maximal helicity violating (MHV) amplitudes in N = 4 super Yang-Mills (SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and Witten (CSW). The relations between leading N c amplitudes A n;1 and sub-leading amplitudes A n;c obtained by the CSW prescription are found to be identical to those obtained from conventional field theory calculations. Combining with existing results, this establishes the validity of the CSW prescription to one-loop in the calculation of MHV amplitudes in N = 4 SYM theories of finite N c .

One-loop gauge theory amplitudes in N=4 super Yang–Mills from MHV vertices

Nuclear Physics B, 2005

We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N = 4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N = 4 super Yang-Mills are used as vertices, using an offshell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of supersymmetric MHV one-loop scattering amplitudes with an arbitrary number of external legs in N = 4 super Yang-Mills. Remarkably, our approach naturally leads to a representation of the amplitudes as dispersion integrals, which we evaluate exactly. This yields a new, simplified form for the MHV amplitudes, which is equivalent to the expressions obtained previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.

T-duality to scattering amplitude and Wilson loop in non-commutative super Yang-Mills theory

Journal of High Energy Physics, 2018

We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed AdS 5×S 5 spacetime, which corresponds to 4D mathcalN=4\mathcal{N}=4mathcalN=4 N = 4 non-commutative super Yang-Mills theory (NCSYM). We then construct the solution to Killing spinor equations of the resulting background, and perform the fermionic T-duality transformation. The final dual geometry becomes the usual AdS 5 × S 5 spacetime but with a constant NS-NS B-field depending on the non-commutative parameter. As applications, we study the gluon scattering amplitude and open string (Wilson loop) solution in the TsT-deformed AdS 5 × S 5 spacetime, which are dual to the null polygon Wilson loop and the folded string solution respectively in the final dual geometry.

S-Duality and Helicity Amplitudes

We examine interacting Abelian theories at low energies and show that holomorphically normalized photon helicity amplitudes transform into dual amplitudes under SL(2, Z) as modular forms with weights that depend on the number of positive and negative helicity photons and on the number of internal photon lines. Moreover, canonically normalized helicity amplitudes transform by a phase, so that even though the amplitudes are not duality invariant, their squares are duality invariant. We explicitly verify the duality transformation at one loop by comparing the amplitudes in the case of an electron and the dyon that is its SL(2, Z) image, and extend the invariance of squared amplitudes order by order in perturbation theory. We demonstrate that S-duality is property of all low-energy effective Abelian theories with electric and/or magnetic charges and see how the duality generically breaks down at high energies.

N = 2 worldsheet instantons yield cubic self-dual Yang-Mills

Physics Letters B, 1997

When the gauge instantons on the N=2 string worldsheet are properly included in the sum over topologies, the breaking of SO(2, 2) Lorentz symmetry in R 2,2 is parametrized by a spacetime twistor containing the string coupling and theta angle. The resulting (tree-level) effective action for the open string is not Yang's but Leznov's cubic action for self-dual Yang-Mills in a lightcone gauge. In the closed case, Plebański's action for self-dual gravity gets modified analogously. In contrast to the N=1 NSR string, picture-changing is not locally invertible, but produces a semi-infinite tower of massless physical states with ever-increasing spin, perhaps related to harmonic superspace. A truncation yields the two-field action of Chalmers and Siegel.

The soft-collinear bootstrap: Yang-Mills amplitudes at six- and seven-loops

2012

Infrared divergences in scattering amplitudes arise when a loop momentum becomes collinear with a massless external momentum p. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in N = 4 super-Yang-Mills theory enjoy softer than expected behavior as p already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any loop-order, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation, we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary looporder. The six-and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively.

Instanton calculus, topological field theories and N = 2 super Yang-Mills theories

Journal of High Energy Physics, 2000

The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N = 2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N = 2 Super Yang-Mills theory. After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. As a consequence, instanton-dominated Green's functions in N = 2 Super Yang-Mills can be equivalently computed either using the constrained instanton method or making reference to the topological twisted version of the theory. We explicitly compute the instanton measure and the contribution to u = Trφ 2 for winding numbers one and two. We then show that each non-perturbative contribution to the N = 2 low-energy effective action can be written as the integral of a total derivative of a function of the instanton moduli. Only instanton configurations of zero conformal size contribute to this result. Finally, the 8k-dimensional instanton moduli space is built using the hyperkähler quotient procedure, which clarifies the geometrical meaning of our approach.