Duals of U(N) LGT with staggered fermions

TL;DR

This paper reviews dual formulations of non-abelian lattice gauge theories, focusing on U(N) models, and introduces a dual representation using Weingarten functions applicable in various dimensions and conditions.

Contribution

It presents a novel dual formulation for U(N) lattice gauge theories using Weingarten functions, covering pure gauge, strong coupling, and two-dimensional QCD with staggered fermions.

Findings

Dual representations constructed for pure gauge models in all dimensions.

Dual formulations developed for strong coupling limits with multiple flavors.

Application discussions for finite temperature/density QCD.

Abstract

Various approaches to construction of dual formulations of non-abelian lattice gauge theories are reviewed. In the case of U(N) LGT we use a theory of the Weingarten functions to construct a dual formulation. In particular, the dual representations are constructed 1) for pure gauge models in all dimensions, 2) in the strong coupling limit for the models with arbitrary number of flavours and 3) for two-dimensional U(N) QCD with staggered fermions. Applications related to the finite temperature/density QCD are discussed.