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Papers by Zachary Guralnik

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, 2001

Journal of High Energy Physics, 2002

Arxiv preprint hep-th/9612079, 1996

Journal of High Energy Physics, 2001

Neutrino Mass, Dark Matter, Gravitational Waves, Monopole Condensation, and Light Cone Quantization, 1996

ABSTRACT this paper. Most of the details will appear elsewhere. The naive resolution of the probl... more ABSTRACT this paper. Most of the details will appear elsewhere. The naive resolution of the problem of how to select the boundary conditions is to simply pick the solution which corresponds to the path integral over real fields. However, within certain phases of many theories, it can be shown that the path integral solution is actually not the physical one. Furthermore in some matrix models the integral over real eigenvalues is not even convergent because of negative couplings. This forces the consideration of "exotic" solutions of the Schwinger--Dyson equations which have integral representations involving sums of integrals of the fields over various inequivalent complex contours. For theories with a local order parameter, symmetry breaking solutions are generated naturally by choosing a symmetry breaking set of contours. In the conventional approach to obtaining the broken phase, the real contour is chosen but a small symmetry breaking term is added to the action. This term is removed only after taking a thermodynamic limit, in which the number of degrees of freedom becomes infinite. In fact one can also obtain the broken phase by choosing a symmetry breaking boundary condition (contour) and then taking the thermodynamic limit directly. This is a simple example showing that the exotic solutions are not necessarily unphysical. We conjecture that this is true even for theories with a nonlocal order parameter, though this has yet to be demonstrated. The difficulty in choosing the correct boundary conditions lies in the fact that there are so many of them. Furthermore since the Schwinger--Dyson equations satisfied by the partition function are linear, there naively appears to be a continuum of mixed phases, which does not make physical sense. Most of this problem is resolved by ...

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

We discuss the relationship between the boundary conditions of the Schwinger-Dyson equations and ... more We discuss the relationship between the boundary conditions of the Schwinger-Dyson equations and the phase diagram of a bosonic field theory or matrix model. In the thermodynamic limit, many boundary conditions lead to the same solution, while other boundary conditions have no such limit. The list of boundary conditions for which a thermodynamic limit exists depends on the parameters of the theory. The boundary conditions of a physical solution may be quite exotic, corresponding to path integration over various inequivalent complex contours.

We find aspects of electrically confining large NNN Yang-Mills theories on T2timesRd−2T^2 \times R^{d-2}T2timesRd−2 w... more We find aspects of electrically confining large NNN Yang-Mills theories on T2timesRd−2T^2 \times R^{d-2}T2timesRd−2 which are consistent with a GL(2,Z)GL(2,Z)GL(2,Z) duality. The modular parameter associated with this GL(2,Z)GL(2,Z)GL(2,Z) is given by moverN+iLambda2A{m\over N} + i\Lambda^2 AmoverN+iLambda2A, where AAA is the area of the torus, mmm is the t'Hooft twist on the torus, and Lambda2\Lambda^2Lambda2 is the string tension. NNN is taken to infinity keeping moverNm\over NmoverN and g2Ng^2Ng2N fixed. This duality may be interpreted as T-duality of the QCD string if one identifies the magnetic flux with a two-form background in the string theory. Our arguments make no use of supersymmetry. While we are not able to show that this is an exact self duality of conventional QCD, we conjecture that it may be applicable within the universality class of QCD. We discuss the status of the conjecture for the soluble case of pure two dimensional Euclidean QCD on T2T^2T2, which is almost but not exactly self dual. For higher dimensional theories, we discuss qualitative features consist...

Physics of Mass, 2002

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

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2014

We describe classes of ergodic dynamical systems for which some statistical properties are known ... more We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This definition generalizes the construction of Hamiltonian systems by a Hamiltonian and a symplectic form. Some low dimensional examples are given, as well as a discretized field theory with a large number of degrees of freedom and a local nearest neighbor interaction. We also evaluate unequal-time correlations of these systems without direct numerical simulation, by Padé approximants of a short-time expansion. We briefly speculate on the possibility of constructing chaotic dynamical systems with non-integer dimension and exactly known statistics. In this case there is no probability density, suggesting an alternative construction in terms of a Hopf characteristic function and a two-form.

We calculate the αs corrections to the form factors which parameterize the hadronic tensor releva... more We calculate the αs corrections to the form factors which parameterize the hadronic tensor relevant for inclusive semileptonic B → Xτν� andb → Xτν� decays. We apply our results to the double differential decay rates for the decays of B mesons and polarized �b baryons to polarized τ leptons, presenting them in terms of one-dimensional integrals. Formulas appropriate for insertion

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 Theta. For such values of Theta, there are Morita equivalent descriptions in terms of Yang-Mills theories on commutative tori with very different magnetic fluxes and rank. In

Journal of High Energy Physics, 2001

Journal of High Energy Physics, 2011

Journal of High Energy Physics, 2005

Journal of High Energy Physics, 2005

Journal of High Energy Physics, 2000

Journal of High Energy Physics, 2004

... ik@physik.hu-berlin.de Robert Helling Department for Applied Mathematics and Theoretical Phys... more ... ik@physik.hu-berlin.de Robert Helling Department for Applied Mathematics and Theoretical Physics, Cambridge University Wilberforce Road, Cambridge CW3 0WA, UK E-mail: helling@atdotde.de Abstract: We study brane ...

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, 2001

Journal of High Energy Physics, 2002

Arxiv preprint hep-th/9612079, 1996

Journal of High Energy Physics, 2001

Neutrino Mass, Dark Matter, Gravitational Waves, Monopole Condensation, and Light Cone Quantization, 1996

ABSTRACT this paper. Most of the details will appear elsewhere. The naive resolution of the probl... more ABSTRACT this paper. Most of the details will appear elsewhere. The naive resolution of the problem of how to select the boundary conditions is to simply pick the solution which corresponds to the path integral over real fields. However, within certain phases of many theories, it can be shown that the path integral solution is actually not the physical one. Furthermore in some matrix models the integral over real eigenvalues is not even convergent because of negative couplings. This forces the consideration of "exotic" solutions of the Schwinger--Dyson equations which have integral representations involving sums of integrals of the fields over various inequivalent complex contours. For theories with a local order parameter, symmetry breaking solutions are generated naturally by choosing a symmetry breaking set of contours. In the conventional approach to obtaining the broken phase, the real contour is chosen but a small symmetry breaking term is added to the action. This term is removed only after taking a thermodynamic limit, in which the number of degrees of freedom becomes infinite. In fact one can also obtain the broken phase by choosing a symmetry breaking boundary condition (contour) and then taking the thermodynamic limit directly. This is a simple example showing that the exotic solutions are not necessarily unphysical. We conjecture that this is true even for theories with a nonlocal order parameter, though this has yet to be demonstrated. The difficulty in choosing the correct boundary conditions lies in the fact that there are so many of them. Furthermore since the Schwinger--Dyson equations satisfied by the partition function are linear, there naively appears to be a continuum of mixed phases, which does not make physical sense. Most of this problem is resolved by ...

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

We discuss the relationship between the boundary conditions of the Schwinger-Dyson equations and ... more We discuss the relationship between the boundary conditions of the Schwinger-Dyson equations and the phase diagram of a bosonic field theory or matrix model. In the thermodynamic limit, many boundary conditions lead to the same solution, while other boundary conditions have no such limit. The list of boundary conditions for which a thermodynamic limit exists depends on the parameters of the theory. The boundary conditions of a physical solution may be quite exotic, corresponding to path integration over various inequivalent complex contours.

We find aspects of electrically confining large NNN Yang-Mills theories on T2timesRd−2T^2 \times R^{d-2}T2timesRd−2 w... more We find aspects of electrically confining large NNN Yang-Mills theories on T2timesRd−2T^2 \times R^{d-2}T2timesRd−2 which are consistent with a GL(2,Z)GL(2,Z)GL(2,Z) duality. The modular parameter associated with this GL(2,Z)GL(2,Z)GL(2,Z) is given by moverN+iLambda2A{m\over N} + i\Lambda^2 AmoverN+iLambda2A, where AAA is the area of the torus, mmm is the t'Hooft twist on the torus, and Lambda2\Lambda^2Lambda2 is the string tension. NNN is taken to infinity keeping moverNm\over NmoverN and g2Ng^2Ng2N fixed. This duality may be interpreted as T-duality of the QCD string if one identifies the magnetic flux with a two-form background in the string theory. Our arguments make no use of supersymmetry. While we are not able to show that this is an exact self duality of conventional QCD, we conjecture that it may be applicable within the universality class of QCD. We discuss the status of the conjecture for the soluble case of pure two dimensional Euclidean QCD on T2T^2T2, which is almost but not exactly self dual. For higher dimensional theories, we discuss qualitative features consist...

Physics of Mass, 2002

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

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2014

We describe classes of ergodic dynamical systems for which some statistical properties are known ... more We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This definition generalizes the construction of Hamiltonian systems by a Hamiltonian and a symplectic form. Some low dimensional examples are given, as well as a discretized field theory with a large number of degrees of freedom and a local nearest neighbor interaction. We also evaluate unequal-time correlations of these systems without direct numerical simulation, by Padé approximants of a short-time expansion. We briefly speculate on the possibility of constructing chaotic dynamical systems with non-integer dimension and exactly known statistics. In this case there is no probability density, suggesting an alternative construction in terms of a Hopf characteristic function and a two-form.

We calculate the αs corrections to the form factors which parameterize the hadronic tensor releva... more We calculate the αs corrections to the form factors which parameterize the hadronic tensor relevant for inclusive semileptonic B → Xτν� andb → Xτν� decays. We apply our results to the double differential decay rates for the decays of B mesons and polarized �b baryons to polarized τ leptons, presenting them in terms of one-dimensional integrals. Formulas appropriate for insertion

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 Theta. For such values of Theta, there are Morita equivalent descriptions in terms of Yang-Mills theories on commutative tori with very different magnetic fluxes and rank. In

Journal of High Energy Physics, 2001

Journal of High Energy Physics, 2011

Journal of High Energy Physics, 2005

Journal of High Energy Physics, 2005

Journal of High Energy Physics, 2000

Journal of High Energy Physics, 2004

... ik@physik.hu-berlin.de Robert Helling Department for Applied Mathematics and Theoretical Phys... more ... ik@physik.hu-berlin.de Robert Helling Department for Applied Mathematics and Theoretical Physics, Cambridge University Wilberforce Road, Cambridge CW3 0WA, UK E-mail: helling@atdotde.de Abstract: We study brane ...