Zachary Guralnik - Academia.edu (original) (raw)
Papers by Zachary Guralnik
Picard-Lefschetz theory is applied to solutions of the Helmholtz equation, formulated in terms of... more Picard-Lefschetz theory is applied to solutions of the Helmholtz equation, formulated in terms of sums of integrals of a proper-time, or `einbein', wave function Ψ(Λ)=exp(imathbbS(Λ))Ψ(Λ) = \exp(i\mathbb S(Λ))Ψ(Λ)=exp(imathbbS(Λ)) along complex contours bounded by essential singularities of ΨΨΨ, or poles of mathbbS\mathbb SmathbbS. There is a one to one map between steepest descent paths connecting poles, also known as Lefschetz thimbles, and both real and complex eigenrays. Residues of poles at finite ΛΛΛ always vanish at some spatial points, which correspond to the location of a source if only one Lefschetz thimble is bounded at the pole. If there are two oppositely oriented contours ending at a pole, points of vanishing residue are not source locations, but are argued to be the locus on which caustic curves may have singularities such as cusps. The map between mathbbS\mathbb SmathbbS and the generating function in the Thom--Arnold classification of catastrophes is discussed. Monodromies of the solution set with respect to complexified par...
We study strong coupling phenomena in U(1) gauge theory on the non-commutative plane. To do so, w... more We study strong coupling phenomena in U(1) gauge theory on the non-commutative plane. To do so, we make use of a T-dual description in terms of an N → ∞ limit of U(N) gauge theory on a commutative torus. The magnetic flux on this torus is taken to be m = N − 1, while the area scales like 1/N, keeping Λ QCD fixed. With a few assumptions, we argue that the speed of high frequency light in pure non-commutative QED is modified in the non-commutative directions by the factor 1 + Λ 4 QCD θ 2 , where θ is the non-commutative parameter. If charged flavours are included, there is an upper bound on the momentum of a photon propagating in the non-commutative directions, beyond which it is unstable against production of charged pairs. We also discuss a particular θ → ∞ limit of pure non-commutative QED which is T-dual to a more conventional N → ∞ limit with m/N fixed. In the non-commutative description, this limit gives rise to an exotic theory of open strings.
Neutrino Mass, Dark Matter, Gravitational Waves, Monopole Condensation, and Light Cone Quantization, 1996
Physics of Mass
We have given evidence that large N confining Yang Mills theories on tori may have an SL(2,Z) dua... more We have given evidence that large N confining Yang Mills theories on tori may have an SL(2,Z) duality which appears to be T-duality of a string description. The existence of such a duality would be quite useful, since it relates non compact 4 dimensional theories to more numerically tractable 2 dimensional theories. It should be interesting to study the two
Journal of High Energy Physics, 2001
We study aspects of gauge theory on tori which are a consequences of Morita equivalence. In parti... more We study aspects of gauge theory on tori which are a consequences of Morita equivalence. In particular we study the behavior of gauge theory on non-commutative tori for arbitrarily close rational values of Θ. For such values of Θ, there are Morita equivalent descriptions in terms of Yang-Mills theories on commutative tori with very different magnetic fluxes and rank. In order for the correlators of open Wilson lines to depend smoothly on Θ, the correlators of closed Wilson lines in the commutative Yang-Mills theory must satisfy strong constraints. If exactly satisfied, these constraints give relations between small and large N gauge theories. We verify that these constraints are obeyed at leading order in the 1/N expansion of pure 2-d QCD and of strongly coupled N = 4 super Yang-Mills theory.
Nuclear Physics B, 1998
The moduli space of 0-branes on T 4 gives a prediction for the moduli space of torons in U (n) Su... more The moduli space of 0-branes on T 4 gives a prediction for the moduli space of torons in U (n) Super Yang Mills theory which preserve 16 supersymmetries. The zero brane number corresponds to the greatest common denominator of the rank n, magnetic fluxes and the instanton number. This prediction is derived using U-duality. We explicitly check this prediction by analyzing U (n) bundles with non-zero first as well as second Chern classes. The argument is extended to deduce the moduli space of torons which preserve 8 supersymmetries. Parts of the discussion extend naturally to T 2 and T 3. Some of the U-dualities involved are related to Lorentz boosts along the eleventh direction in M theory.
Journal of High Energy Physics, 2005
We present a proposal for the description of the Higgs branch of four-dimensional N =2 supersymme... more We present a proposal for the description of the Higgs branch of four-dimensional N =2 supersymmetric Yang-Mills theories in the context of the AdS/CFT correspondence. We focus on a finite Sp(N) N =2 theory arising as dual of a configuration of N D3-branes in the vicinity of four D7-branes and an orientifold 7-plane in type I ′ string theory. The field theory contains hypermultiplets in the second rank anti-symmetric and in the fundamental representations. The Higgs branch has a dual description in terms of gauge field configurations with non-zero instanton number on the world-volume of the D7-branes. In this setting the non-renormalisation of the metric on the Higgs branch implies constraints on the α ′ corrections to the D7-brane effective action, including couplings to the curvature and five-form field strength. In the second part of the paper we discuss non-renormalisation properties of BPS Wilson lines, which are closely related to the physics of the Higgs branch. Using a formulation of the four-dimensional N =2 theory in terms of a three-dimensional N =2 superspace we show that the expectation value of certain Wilson-line operators with hypermultiplets at the end points is independent of the length and thus coincides with the expectation value of the local operators parametrising the Higgs branch.
Journal of High Energy Physics, 2000
We study discrete fluxes in four dimensional SU (N) gauge theories with a mass gap by using brane... more We study discrete fluxes in four dimensional SU (N) gauge theories with a mass gap by using brane compactifications which give N = 1 or N = 0 supersymmetry. We show that when such theories are compactified further on a torus, the t'Hooft magnetic flux m is related to the NS two-form modulus B by B = 2π m N. These values of B label degenerate brane vacua, giving a simple demonstration of magnetic screening. Furthermore, for these values of B one has a conventional gauge theory on a commutative torus, without having to perform any T-dualities. Because of the mass gap, a generic B does not give a four dimensional gauge theory on a non-commutative torus. The Kaluza-Klein modes which must be integrated out to give a four dimensional theory decouple only when B = 2π m N. Finally we show that 2π m N behaves like a two form modulus of the QCD string. This confirms a previous conjecture based on properties of large N QCD suggesting a T-duality invariance.
Journal of High Energy Physics, 2002
Physics Letters B, 2001
The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the pres... more The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into their lowest Landau level, and renders the fluid dynamics non-commutative, with a Moyal product determined by the background magnetic field.
Nuclear Physics B, 2006
We construct the dual supergravity description of strongly coupled, large N , eightsupercharge ga... more We construct the dual supergravity description of strongly coupled, large N , eightsupercharge gauge theories with fundamental hypermultiplets at points on the mixed Coulomb-Higgs branch. With certain assumptions about unknown couplings of D-branes to supergravity, this construction gives the correct metric on the hypermultiplet (Higgs-branch) component the moduli space, which decouples from the vector multiplet (Coulomb-branch) moduli. Going beyond the geodesic approximation, we find that the dynamics of a hypermultiplet VEV rolling towards a singularity on the Higgs component of the moduli space is sensitive to the vector multiplet moduli. The dual description of the approach to the singularity involves collapsing "instantons" of a non-Abelian Dirac-Born-Infeld theory in a curved background. In general, we find a decelerating approach to the singularity, although the manner of deceleration depends on the vector multiplet moduli. Upon introducing a potential on the Higgs branch of a four dimensional N = 2 theory coupled to gravity, this deceleration mechanism might lead to interesting inflating cosmologies analogous those studied recently by Alishahiha, Silverstein and Tong.
The Journal of the Acoustical Society of America, 2013
Deep ocean acoustics, in the absence of shipping and wildlife, is driven by surface processes. Be... more Deep ocean acoustics, in the absence of shipping and wildlife, is driven by surface processes. Best understood is the signal generated by non-linear surface wave interactions, the Longuet-Higgins mechanism, which dominates from 0.1 to 10 Hz, and may be significant for another octave. For this source, the spectral matrix of pressure and vector velocity is derived for points near the bottom of a deep ocean resting on an elastic half-space. In the absence of a bottom, the ratios of matrix elements are universal constants. Bottom effects vitiate the usual "standing wave approximation," but a weaker form of the approximation is shown to hold, and this is used for numerical calculations. In the weak standing wave approximation, the ratios of matrix elements are independent of the surface wave spectrum, but depend on frequency and the propagation environment. Data from the Hawaii-2 Observatory are in excellent accord with the theory for frequencies between 0.1 and 1 Hz, less so at higher frequencies. Insensitivity of the spectral ratios to wind, and presumably waves, is indeed observed in the data.
The Journal of the Acoustical Society of America, 2010
ABSTRACT Very low-frequency, deep ocean ambient noise is generated by non-linear interactions (co... more ABSTRACT Very low-frequency, deep ocean ambient noise is generated by non-linear interactions (collisions) between surface waves with nearly equal frequency, propagating in nearly opposite direction. It is shown that the usual "standing wave" approximation used to compute this noise predicts that the ratios of entries in the power spectral density matrix, obtained from auto and cross-correlations of acoustic velocity and pressure fluctuations, are universal constants. This prediction is too strong and not observed. A careful consideration of bottom effects invalidates the standing wave approximation. Nevertheless a weak version of the standing wave approximation still holds and has interesting implications. While the ratios of entries in the power spectral density matrix due to surface wave generated noise are not universal constants, they are insensitive to the details of the surface wave spectrum. This theoretical prediction is borne out by data from the Hawaii-2 Observatory. [Work supported by ONR.].
Fortschritte der Physik, 2005
We construct the AdS description of the Higgs branch of the finite N = 2 Sp(N) gauge theory with ... more We construct the AdS description of the Higgs branch of the finite N = 2 Sp(N) gauge theory with one antisymmetric hypermultiplet and four fundamental hypermultiplets. Holography, combined with the non-renormalization of the metric on the Higgs branch, leads to novel constraints on unknown terms in the non-abelian Dirac-Born-Infeld action. These terms include non-minimal couplings of D-branes to bulk supergravity fields.
Arxiv preprint hep-th/9903021, 1999
We argue that non-supersymmetric large N QCD compactified on T 2 exhibits properties characterist... more We argue that non-supersymmetric large N QCD compactified on T 2 exhibits properties characteristic of an SL(2, Z) T-duality. The kahler structure on which this SL(2, Z) acts is given by m N + iΛ 2 A, where A is the area of the torus, m is the 't Hooft magnetic flux on the torus, and Λ 2 is the QCD string tension.
arXiv: High Energy Physics - Theory, 2018
We study the large source asymptotics of the generating functional in quantum field theory using ... more We study the large source asymptotics of the generating functional in quantum field theory using the holographic renormalization group, and draw comparisons with the asymptotics of the Hopf characteristic function in fractal geometry. Based on the asymptotic behavior, we find a correspondence relating the Weyl anomaly and the fractal dimension of the Euclidean path integral measure. We are led to propose an equivalence between the logarithmic ultraviolet divergence of the Shannon entropy of this measure and the integrated Weyl anomaly, reminiscent of a known relation between logarithmic divergences of entanglement entropy and a central charge. It follows that the information dimension associated with the Euclidean path integral measure satisfies a c-theorem.
Journal of High Energy Physics, 2002
We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. Fo... more We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational θ, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous N × N symmetry breaking in the Morita dual SU (N) theory due to electric flux condensation.
Journal of High Energy Physics, 2001
We present explicit methods for computing the discriminant curves and the associated Kodaira type... more We present explicit methods for computing the discriminant curves and the associated Kodaira type fiber degeneracies of elliptically fibered Calabi-Yau threefolds. These methods are applied to a specific three-family, SU (5) grand unified theory of particle physics within the context of Heterotic M-Theory. It is demonstrated that there is always a region of moduli space where a bulk space five-brane is wrapped on a pure fiber in the Calabi-Yau threefold. Restricting the discussion to the smooth parts of the discriminant curve, we explore the properties of the N = 2 BPS supermultiplets that arise on the worldvolume of this five-brane due to the degeneration of the elliptic fiber. The associated degenerating M membranes are shown to project to string junctions in the base space. We use string junction techniques to explicitly compute the light BPS hyper-and vector multiplet spectrum for each Kodaira type fiber near the smooth part of the discriminant curve in the SU (5) GUT theory.
Journal of High Energy Physics, 2011
We use Lorentzian signature AdS/CFT duality to study a first order phase transition in strongly c... more We use Lorentzian signature AdS/CFT duality to study a first order phase transition in strongly coupled gauge theories which is akin to the chiral phase transition in QCD. We discuss the relation between the latent heat and the energy (suitably defined) of the component of a D-brane which lies behind the horizon at the critical temperature. A numerical simulation of a dynamical phase transition in an expanding, cooling Quark-Gluon plasma produced in a relativistic collision is carried out.
Journal of High Energy Physics, 2002
In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near... more In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near the smooth part of the discriminant curve. In this paper, we extend that work to compute the light states on the worldvolume of five-branes wrapped on fibers near certain singular loci of the discriminant. We regulate the singular behavior near these loci by deforming the discriminant curve and expressing the singularity in terms of knots and their associated braids. There braids allow us to compute the appropriate string junction lattice for the singularity and,hence to determine the spectrum of light BPS states. We find that these techniques are valid near singular points with N = 2 supersymmetry.
Picard-Lefschetz theory is applied to solutions of the Helmholtz equation, formulated in terms of... more Picard-Lefschetz theory is applied to solutions of the Helmholtz equation, formulated in terms of sums of integrals of a proper-time, or `einbein', wave function Ψ(Λ)=exp(imathbbS(Λ))Ψ(Λ) = \exp(i\mathbb S(Λ))Ψ(Λ)=exp(imathbbS(Λ)) along complex contours bounded by essential singularities of ΨΨΨ, or poles of mathbbS\mathbb SmathbbS. There is a one to one map between steepest descent paths connecting poles, also known as Lefschetz thimbles, and both real and complex eigenrays. Residues of poles at finite ΛΛΛ always vanish at some spatial points, which correspond to the location of a source if only one Lefschetz thimble is bounded at the pole. If there are two oppositely oriented contours ending at a pole, points of vanishing residue are not source locations, but are argued to be the locus on which caustic curves may have singularities such as cusps. The map between mathbbS\mathbb SmathbbS and the generating function in the Thom--Arnold classification of catastrophes is discussed. Monodromies of the solution set with respect to complexified par...
We study strong coupling phenomena in U(1) gauge theory on the non-commutative plane. To do so, w... more We study strong coupling phenomena in U(1) gauge theory on the non-commutative plane. To do so, we make use of a T-dual description in terms of an N → ∞ limit of U(N) gauge theory on a commutative torus. The magnetic flux on this torus is taken to be m = N − 1, while the area scales like 1/N, keeping Λ QCD fixed. With a few assumptions, we argue that the speed of high frequency light in pure non-commutative QED is modified in the non-commutative directions by the factor 1 + Λ 4 QCD θ 2 , where θ is the non-commutative parameter. If charged flavours are included, there is an upper bound on the momentum of a photon propagating in the non-commutative directions, beyond which it is unstable against production of charged pairs. We also discuss a particular θ → ∞ limit of pure non-commutative QED which is T-dual to a more conventional N → ∞ limit with m/N fixed. In the non-commutative description, this limit gives rise to an exotic theory of open strings.
Neutrino Mass, Dark Matter, Gravitational Waves, Monopole Condensation, and Light Cone Quantization, 1996
Physics of Mass
We have given evidence that large N confining Yang Mills theories on tori may have an SL(2,Z) dua... more We have given evidence that large N confining Yang Mills theories on tori may have an SL(2,Z) duality which appears to be T-duality of a string description. The existence of such a duality would be quite useful, since it relates non compact 4 dimensional theories to more numerically tractable 2 dimensional theories. It should be interesting to study the two
Journal of High Energy Physics, 2001
We study aspects of gauge theory on tori which are a consequences of Morita equivalence. In parti... more We study aspects of gauge theory on tori which are a consequences of Morita equivalence. In particular we study the behavior of gauge theory on non-commutative tori for arbitrarily close rational values of Θ. For such values of Θ, there are Morita equivalent descriptions in terms of Yang-Mills theories on commutative tori with very different magnetic fluxes and rank. In order for the correlators of open Wilson lines to depend smoothly on Θ, the correlators of closed Wilson lines in the commutative Yang-Mills theory must satisfy strong constraints. If exactly satisfied, these constraints give relations between small and large N gauge theories. We verify that these constraints are obeyed at leading order in the 1/N expansion of pure 2-d QCD and of strongly coupled N = 4 super Yang-Mills theory.
Nuclear Physics B, 1998
The moduli space of 0-branes on T 4 gives a prediction for the moduli space of torons in U (n) Su... more The moduli space of 0-branes on T 4 gives a prediction for the moduli space of torons in U (n) Super Yang Mills theory which preserve 16 supersymmetries. The zero brane number corresponds to the greatest common denominator of the rank n, magnetic fluxes and the instanton number. This prediction is derived using U-duality. We explicitly check this prediction by analyzing U (n) bundles with non-zero first as well as second Chern classes. The argument is extended to deduce the moduli space of torons which preserve 8 supersymmetries. Parts of the discussion extend naturally to T 2 and T 3. Some of the U-dualities involved are related to Lorentz boosts along the eleventh direction in M theory.
Journal of High Energy Physics, 2005
We present a proposal for the description of the Higgs branch of four-dimensional N =2 supersymme... more We present a proposal for the description of the Higgs branch of four-dimensional N =2 supersymmetric Yang-Mills theories in the context of the AdS/CFT correspondence. We focus on a finite Sp(N) N =2 theory arising as dual of a configuration of N D3-branes in the vicinity of four D7-branes and an orientifold 7-plane in type I ′ string theory. The field theory contains hypermultiplets in the second rank anti-symmetric and in the fundamental representations. The Higgs branch has a dual description in terms of gauge field configurations with non-zero instanton number on the world-volume of the D7-branes. In this setting the non-renormalisation of the metric on the Higgs branch implies constraints on the α ′ corrections to the D7-brane effective action, including couplings to the curvature and five-form field strength. In the second part of the paper we discuss non-renormalisation properties of BPS Wilson lines, which are closely related to the physics of the Higgs branch. Using a formulation of the four-dimensional N =2 theory in terms of a three-dimensional N =2 superspace we show that the expectation value of certain Wilson-line operators with hypermultiplets at the end points is independent of the length and thus coincides with the expectation value of the local operators parametrising the Higgs branch.
Journal of High Energy Physics, 2000
We study discrete fluxes in four dimensional SU (N) gauge theories with a mass gap by using brane... more We study discrete fluxes in four dimensional SU (N) gauge theories with a mass gap by using brane compactifications which give N = 1 or N = 0 supersymmetry. We show that when such theories are compactified further on a torus, the t'Hooft magnetic flux m is related to the NS two-form modulus B by B = 2π m N. These values of B label degenerate brane vacua, giving a simple demonstration of magnetic screening. Furthermore, for these values of B one has a conventional gauge theory on a commutative torus, without having to perform any T-dualities. Because of the mass gap, a generic B does not give a four dimensional gauge theory on a non-commutative torus. The Kaluza-Klein modes which must be integrated out to give a four dimensional theory decouple only when B = 2π m N. Finally we show that 2π m N behaves like a two form modulus of the QCD string. This confirms a previous conjecture based on properties of large N QCD suggesting a T-duality invariance.
Journal of High Energy Physics, 2002
Physics Letters B, 2001
The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the pres... more The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into their lowest Landau level, and renders the fluid dynamics non-commutative, with a Moyal product determined by the background magnetic field.
Nuclear Physics B, 2006
We construct the dual supergravity description of strongly coupled, large N , eightsupercharge ga... more We construct the dual supergravity description of strongly coupled, large N , eightsupercharge gauge theories with fundamental hypermultiplets at points on the mixed Coulomb-Higgs branch. With certain assumptions about unknown couplings of D-branes to supergravity, this construction gives the correct metric on the hypermultiplet (Higgs-branch) component the moduli space, which decouples from the vector multiplet (Coulomb-branch) moduli. Going beyond the geodesic approximation, we find that the dynamics of a hypermultiplet VEV rolling towards a singularity on the Higgs component of the moduli space is sensitive to the vector multiplet moduli. The dual description of the approach to the singularity involves collapsing "instantons" of a non-Abelian Dirac-Born-Infeld theory in a curved background. In general, we find a decelerating approach to the singularity, although the manner of deceleration depends on the vector multiplet moduli. Upon introducing a potential on the Higgs branch of a four dimensional N = 2 theory coupled to gravity, this deceleration mechanism might lead to interesting inflating cosmologies analogous those studied recently by Alishahiha, Silverstein and Tong.
The Journal of the Acoustical Society of America, 2013
Deep ocean acoustics, in the absence of shipping and wildlife, is driven by surface processes. Be... more Deep ocean acoustics, in the absence of shipping and wildlife, is driven by surface processes. Best understood is the signal generated by non-linear surface wave interactions, the Longuet-Higgins mechanism, which dominates from 0.1 to 10 Hz, and may be significant for another octave. For this source, the spectral matrix of pressure and vector velocity is derived for points near the bottom of a deep ocean resting on an elastic half-space. In the absence of a bottom, the ratios of matrix elements are universal constants. Bottom effects vitiate the usual "standing wave approximation," but a weaker form of the approximation is shown to hold, and this is used for numerical calculations. In the weak standing wave approximation, the ratios of matrix elements are independent of the surface wave spectrum, but depend on frequency and the propagation environment. Data from the Hawaii-2 Observatory are in excellent accord with the theory for frequencies between 0.1 and 1 Hz, less so at higher frequencies. Insensitivity of the spectral ratios to wind, and presumably waves, is indeed observed in the data.
The Journal of the Acoustical Society of America, 2010
ABSTRACT Very low-frequency, deep ocean ambient noise is generated by non-linear interactions (co... more ABSTRACT Very low-frequency, deep ocean ambient noise is generated by non-linear interactions (collisions) between surface waves with nearly equal frequency, propagating in nearly opposite direction. It is shown that the usual "standing wave" approximation used to compute this noise predicts that the ratios of entries in the power spectral density matrix, obtained from auto and cross-correlations of acoustic velocity and pressure fluctuations, are universal constants. This prediction is too strong and not observed. A careful consideration of bottom effects invalidates the standing wave approximation. Nevertheless a weak version of the standing wave approximation still holds and has interesting implications. While the ratios of entries in the power spectral density matrix due to surface wave generated noise are not universal constants, they are insensitive to the details of the surface wave spectrum. This theoretical prediction is borne out by data from the Hawaii-2 Observatory. [Work supported by ONR.].
Fortschritte der Physik, 2005
We construct the AdS description of the Higgs branch of the finite N = 2 Sp(N) gauge theory with ... more We construct the AdS description of the Higgs branch of the finite N = 2 Sp(N) gauge theory with one antisymmetric hypermultiplet and four fundamental hypermultiplets. Holography, combined with the non-renormalization of the metric on the Higgs branch, leads to novel constraints on unknown terms in the non-abelian Dirac-Born-Infeld action. These terms include non-minimal couplings of D-branes to bulk supergravity fields.
Arxiv preprint hep-th/9903021, 1999
We argue that non-supersymmetric large N QCD compactified on T 2 exhibits properties characterist... more We argue that non-supersymmetric large N QCD compactified on T 2 exhibits properties characteristic of an SL(2, Z) T-duality. The kahler structure on which this SL(2, Z) acts is given by m N + iΛ 2 A, where A is the area of the torus, m is the 't Hooft magnetic flux on the torus, and Λ 2 is the QCD string tension.
arXiv: High Energy Physics - Theory, 2018
We study the large source asymptotics of the generating functional in quantum field theory using ... more We study the large source asymptotics of the generating functional in quantum field theory using the holographic renormalization group, and draw comparisons with the asymptotics of the Hopf characteristic function in fractal geometry. Based on the asymptotic behavior, we find a correspondence relating the Weyl anomaly and the fractal dimension of the Euclidean path integral measure. We are led to propose an equivalence between the logarithmic ultraviolet divergence of the Shannon entropy of this measure and the integrated Weyl anomaly, reminiscent of a known relation between logarithmic divergences of entanglement entropy and a central charge. It follows that the information dimension associated with the Euclidean path integral measure satisfies a c-theorem.
Journal of High Energy Physics, 2002
We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. Fo... more We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational θ, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous N × N symmetry breaking in the Morita dual SU (N) theory due to electric flux condensation.
Journal of High Energy Physics, 2001
We present explicit methods for computing the discriminant curves and the associated Kodaira type... more We present explicit methods for computing the discriminant curves and the associated Kodaira type fiber degeneracies of elliptically fibered Calabi-Yau threefolds. These methods are applied to a specific three-family, SU (5) grand unified theory of particle physics within the context of Heterotic M-Theory. It is demonstrated that there is always a region of moduli space where a bulk space five-brane is wrapped on a pure fiber in the Calabi-Yau threefold. Restricting the discussion to the smooth parts of the discriminant curve, we explore the properties of the N = 2 BPS supermultiplets that arise on the worldvolume of this five-brane due to the degeneration of the elliptic fiber. The associated degenerating M membranes are shown to project to string junctions in the base space. We use string junction techniques to explicitly compute the light BPS hyper-and vector multiplet spectrum for each Kodaira type fiber near the smooth part of the discriminant curve in the SU (5) GUT theory.
Journal of High Energy Physics, 2011
We use Lorentzian signature AdS/CFT duality to study a first order phase transition in strongly c... more We use Lorentzian signature AdS/CFT duality to study a first order phase transition in strongly coupled gauge theories which is akin to the chiral phase transition in QCD. We discuss the relation between the latent heat and the energy (suitably defined) of the component of a D-brane which lies behind the horizon at the critical temperature. A numerical simulation of a dynamical phase transition in an expanding, cooling Quark-Gluon plasma produced in a relativistic collision is carried out.
Journal of High Energy Physics, 2002
In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near... more In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near the smooth part of the discriminant curve. In this paper, we extend that work to compute the light states on the worldvolume of five-branes wrapped on fibers near certain singular loci of the discriminant. We regulate the singular behavior near these loci by deforming the discriminant curve and expressing the singularity in terms of knots and their associated braids. There braids allow us to compute the appropriate string junction lattice for the singularity and,hence to determine the spectrum of light BPS states. We find that these techniques are valid near singular points with N = 2 supersymmetry.