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

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 $S_r$.

arXiv comment16 pages, 3 figures

References in corpus (8)

• SU(N) gauge theories at large N
• Generalizations of some integrals over the unitary group
• On the Complex Asymptotics of the HCIZ and BGW Integrals
• Duals of U(N) LGT with staggered fermions
• Exact Large-Nc Solution of an Effective Theory for Polyakov Loops at Finite Chemical Potential
• Dual formulations of Polyakov loop lattice models
• SU(N) polynomial integrals and some applications
• Integrals over SU(N)

Cited by in corpus (2)

• The Polyakov loop models in the large N limit: Phase diagram at finite density
• Strong coupling methods in QCD thermodynamics