Polyakov Lines in Yang-Mills Matrix Models

TL;DR

This paper analyzes Polyakov lines in Yang-Mills matrix models, providing exact formulas for SU(2), bounds for SU(N), and insights into asymptotic behavior relevant for string theory and gauge theories.

Contribution

It offers the first exact integral formulas for Polyakov lines in SU(2) models and establishes decay bounds for SU(N) models, advancing understanding of their asymptotics.

Findings

Exact integral formulas for SU(2) Polyakov lines

Power-law decay bounds for SU(N) models

Extension methods for correlation functions

Abstract

We study the Polyakov line in Yang-Mills matrix models, which include the IKKT model of IIB string theory. For the gauge group SU(2) we give the exact formulae in the form of integral representations which are convenient for finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper bounds which decay as a power law at large momentum p. We argue that these capture the full asymptotic behaviour. We also indicate how to extend the results to some correlation functions of Polyakov lines.