arXiv subjects

Herbert Neuberger

Publications and source records attributed to Herbert Neuberger.

At least 19 recordsLinked to original sources

arXiv2025

On the momentum of gluons in Lattice Gauge Theory (LGT)

Attempts to improve LGT simulation algorithms by Fourier space preconditioning have been handicapped by the gauge dependence of momenta, familiar from perturbation theory. The continuum theory has a gauge invariant energy-momentum density, indicating this to be a fake obstacle. While perturbation-theory momenta are evidently wrong for the task, momentum-transfer carried by gluons is physical. Simulations using these momenta may become practical in the near future thanks to recent progress in generative models, stochastic and/or deterministic.

hep-lat↗

arXiv2022

Planar diagrams for lattice gauge theory on finite tori

An $N=\infty$ equivalence among quenched $U(N)$ models on finite lattice tori of $V$ sites is proven to all orders in planar perturbation theory by putting circulant lattice momenta together with group indices on 't Hooft's double lines. Known estimates for the number of order $N^2$ diagrams, $N\gg V$, and the simultaneous presence of UV and IR cutoffs, suggest a positive radius of convergence for the planar perturbative expansion before the limit $N=\infty$ is taken.

hep-lat↗

arXiv2022

Deconstructing {\" U}nsal-Yaffe Reconfinement

In the UY reconfined phase on a lattice the thermal trace is over states transforming in all $SU(N)/Z(N)$ irreducible representations as opposed to only over $SU(N)$ singlets in the standard formulation. As $N\to\infty$, on a finite lattice, the usual Hilbert space becomes orthogonal to the deformed one. Concerns about the extended UY proposal for large $N$ Eguchi-Kawai reduction are raised.

hep-lat↗

arXiv2021

Deconstructing finite temperature pure gauge theory

A deconstructed finite temperature gauge theory has the Euclidean time direction kept discrete and finite. The ultraviolet behavior is that of one dimension less than at zero temperature. One can add to the action a gauge invariant term dependent on Polyakov loops, without worrying about nonlocality. The deformation of {\" U}nsal and Yaffe is best analyzed in this framework. It is shown that turning it on causes a dramatic change in the Hilbert space on which the transfer matrix in the temperature direction acts. The undeformed Hilbert space is everywhere a gauge singlet while the deformed one includes all states transforming locally, anywhere, under any SU(N)/Z(N) irreducible representation. Implications of this in the context of large N reduction are discussed.

hep-th↗

arXiv2020

The quenched Eguchi-Kawai model revisited

The motivation and construction of the original Quenched Eguchi-Kawai model are reviewed, providing much greater detail than in the first, 1982 QEK paper. A 2008 article announced that QEK fails as a reduced model because the average over permutations of eigenvalues stays annealed. It is shown here that the original quenching logic naturally leads to a formulation with no annealed average over permutations.

hep-lat↗

arXiv2017

Wavelets and Lattice Field Theory

When continuous fields are expanded in a wavelet basis, a D-dimensional continuum action becomes a (D+1)-dimensional lattice action on the naively discretized Poincare-patch coordinates of an Euclidean AdS(D+1). New possible criteria for acceptable actions open up.

hep-lat↗

arXiv2016

Resolving-Power Quantization

Starting with a general discussion, a program is sketched for a quantization based on dilations. This resolving-power quantization is simplest for scalar field theories. The hope is to find a way to relax the requirement of locality so that the necessity to fine tune mass parameters is eliminated while universality is still preserved.

hep-lat↗

arXiv2015

Scale invariant behavior in a large N matrix model

Eigenvalue distributions of properly regularized Wilson loop operators are used to study the transition from ultra-violet (UV) behavior to infra-red (IR) behavior in gauge theories coupled to matter that potentially have an IR fixed point (FP). We numerically demonstrate emergence of scale invariance in a matrix model that describes $SU(N)$ gauge theory coupled to two flavors of massless adjoint fermions in the large $N$ limit. The eigenvalue distribution of Wilson loops of varying sizes cannot be described by a universal lattice beta-function connecting the UV to the IR.

hep-lat↗

arXiv2014

Lattice radial quantization by cubature

Basic aspects of a program to put field theories quantized in radial coordinates on the lattice are presented. Only scalar fields are discussed. Simple examples are solved to illustrate the strategy when applied to the 3D Ising model.

hep-lat↗

arXiv2014

Polyakov Loop Correlations at Large N

I describe a study of the two-point single-eigenvalue distribution correlation function of Polyakov loops in the confined phase of four dimensional SU(N) YM theory at large N. The reasons for the interest in this correlation function are explained. Analytical and numerical results are presented. Brief conclusions are drawn.

hep-lat↗

arXiv2013

Remarks on correlators of Polyakov Loops

Polyakov loop eigenvalues and their N-dependence are studied in 2 and 4 dimensional SU(N) YM theory. The connected correlation function of the single eigenvalue distributions of two separated Polyakov loops in 2D YM is calculated and is found to have a structure differing from the one of corresponding hermitian random matrix ensembles. No large $N$ non-analyticities are found for two point functions in the confining regime. Suggestions are made for situations in which large-N phase transitions involving Polyakov loops might occur.

hep-lat↗

arXiv2012

Lattice Radial Quantization: 3D Ising

Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known Lagrangians. As an example, we employ a lattice shaped as a cylinder with a 2D Icosahedral cross-section to discretize dilatations in the 3D Ising model. Using this method, we obtain the preliminary estimate eta=0.034(10).

hep-lat↗

arXiv2012

Radial Quantization for Conformal Field Theories on the Lattice

We consider radial quantization for conformal quantum field theory with a lattice regulator. A Euclidean field theory on $\mathbb R^D$ is mapped to a cylindrical manifold, $\mathbb R\times \mathbb S^{D-1}$, whose length is logarithmic in scale separation. To test the approach, we apply this to the 3D Ising model and compute $η$ for the first $Z_2$ odd primary operator.

hep-lat↗

arXiv2012

Large-N string tension from rectangular Wilson loops

In pure SU(N) gauge theory in four dimensions, we determine the string tension at large N from smeared rectangular Wilson loops on the lattice. We learn how well loops of sizes barely on the strong-coupling side of the large-N transition in their eigenvalue distribution can be described by effective string theory.

hep-lat↗

arXiv2012

Rectangular Wilson Loops at Large N

This work is about pure Yang-Mills theory in four Euclidean dimensions with gauge group SU(N). We study rectangular smeared Wilson loops on the lattice at large N and relatively close to the large-N transition point in their eigenvalue density. We show that the string tension can be extracted from these loops but their dependence on shape differs from the asymptotic prediction of effective string theory.

hep-lat↗

arXiv2011

Numerical study of large-N phase transition of smeared Wilson loops in 4D pure YM theory

In Euclidean four-dimensional SU(N) pure gauge theory, eigenvalue distributions of Wilson loop parallel transport matrices around closed spacetime curves show non-analytic behavior (a 'large-N phase transition') at a critical size of the curve. We focus mainly on an observable composed of traces of the Wilson loop operator in all totally antisymmetric representations, which is regularized with the help of smearing. By studying sequences of square Wilson loops on a hypercubic lattice with standard Wilson action, it is shown that this observable has a nontrivial continuum limit as a function of the physical size of the loop. We furthermore present (preliminary) numerical results confirming that, for large N, the N dependence in the critical regime is governed by the universal exponents 1/2 and 3/4 as expected (Burgers universality).

hep-lat↗

arXiv2011

Continuous smearing of Wilson Loops

Continuum smearing was introduced in section 4.1 of JHEP03, 064 (2006) as a meaningful continuum analogue of the well known set of lattice techniques by the same name. Here we apply continuous smearing in continuous space-time to Wilson loops in order to clarify what it does in the context of field theory and also in the context of the loop calculus of the Makeenko-Migdal equation.

hep-lat↗

arXiv2010

The "hard" problem of strong of interactions

This is a write-up of a lecture at the level of a physics colloquium. There exists an idealized mathematical formulation of strong interactions which has no free parameters but is known to describe the real world quite accurately. Over the last three decades the problem has been managed with increasing success. An overview of some facts and a little fiction will be presented, but the question whether the problem can now be considered "easy" will be left unanswered.

hep-lat↗