Finite Volume Gauge Theory Partition Functions in Three Dimensions

TL;DR

This paper derives finite volume partition functions for three-dimensional QCD with various fermion types, revealing new spectral properties and sum rules using effective field theory and extending previous random matrix theory results.

Contribution

It provides a comprehensive derivation of fermion mass dependence in 3D QCD partition functions for all fermion types, extending prior work with new analytical results.

Findings

Derived explicit finite volume partition functions for all fermion types.

Connected partition functions to spectral correlation functions and sum rules.

Extended random matrix theory results to three-dimensional QCD.

Abstract

We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the epsilon-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear sigma-models. New results are given for an arbitrary number of flavours in all three cases of complex, pseudo-real and real fermions, extending some previous considerations based on random matrix theory. They are used to describe the microscopic spectral correlation functions and smallest eigenvalue distributions of the QCD3 Dirac operator, as well as the corresponding massive spectral sum rules.