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 nonzero 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}.
 Publication:

Nuclear Physics B
 Pub Date:
 November 2020
 DOI:
 10.1016/j.nuclphysb.2020.115177
 arXiv:
 arXiv:2008.00773
 Bibcode:
 2020NuPhB.96015177B
 Keywords:

 High Energy Physics  Lattice;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 16 pages, 3 figures