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.
Highlights
Various approaches to construction of dual formulations of non-abelian lattice gauge theories are reviewed
The application of dual representations ranges from the determination of the critical points in the self-dual abelian models to the proof of the confinement in the three-dimensional U(1) lattice gauge theory (LGT) [1, 2] and the numerical study of the U(1) LGT both at zero [3] and at finite temperature [4]
In the strong coupling limit the S U(N) LGT can be mapped onto monomer-dimer-closed baryon loop model [18]
Summary
Dual representations proved to be a very useful concept in the context of abelian spin and gauge models. The sign problem can be fully eliminated in the S U(3) spin model in the complex magnetic field in the flux representation for the partition function [22, 23]. This model is an effective Polyakov loop model which can be calculated from the QCD partition function at strong coupling and large quark masses. In this contribution we present another approach to the duality transformations for U(N) spin and gauge models.
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