The large N limit of SU(N) integrals in lattice models

TL;DR

This paper calculates large N limits of SU(N) and U(N) integrals in lattice models, revealing differences between the groups and discussing implications for SU(N) gauge theories at finite temperature and chemical potential.

Contribution

It introduces a method to compute large N limits of SU(N) integrals using representation theory and sums over partitions, highlighting differences from U(N).

Findings

Large N limit differs between SU(N) and U(N) integrals.

Critical behavior of SU(N) models analyzed.

Implications for finite temperature and chemical potential in lattice gauge theories.

Abstract

The standard U(N) and SU(N) integrals are calculated in the large N limit. Our main finding is that for an important class of integrals this limit is different for two groups. We describe the critical behaviour of SU(N) models and discuss implications of our results for the large N behaviour of SU(N) lattice gauge theories at finite temperatures and non-zero baryon chemical potential. The key ingredients of our approach are 1) expansion of the integrals into a sum over irreducible representations and 2) calculation of sums over partitions of r of products of dimensions of two different representations of a symmetric group $S_r$.