Bootstrap for Finite N Lattice Yang-Mills Theory

TL;DR

This paper develops a bootstrap framework for finite N lattice Yang-Mills theory, efficiently analyzing SU(2) models in multiple dimensions and providing precise bounds consistent with Monte Carlo results.

Contribution

It introduces a linear, convex bootstrap approach for SU(2) lattice Yang-Mills theory, enabling high-precision bounds on physical quantities up to Wilson loops of length 24.

Findings

Bootstrap bounds match Monte Carlo data within 0.1% for free energy per plaquette.

The method provides qualitative estimates of string tension consistent with existing computations.

Efficiently incorporates large Wilson loops due to linearity and convexity of the problem.

Abstract

We introduce a comprehensive framework for analyzing finite $N$ lattice Yang-Mills theory and finite $N$ matrix models. Utilizing this framework, we examine the bootstrap approach to SU(2) Lattice Yang-Mills Theory in 2,3 and 4 dimensions. The SU(2) Makeenko-Migdal loop equations on the lattice are linear and closed exclusively on single-trace Wilson loops. This inherent linearity significantly enhances the efficiency of the bootstrap approach due to the convex nature of the problem, permitting the inclusion of Wilson loops up to length 24. The exact upper and lower margins for the free energy per plaquette, derived from our bootstrap method, demonstrate good agreement with Monte Carlo data, achieving precision within $0.1\%$ for the physically relevant range of couplings in both three and four dimensions. Additionally, our bootstrap data provides estimates of the string tension, in qualitative agreement with existing Monte Carlo computations.