Finite volume gauge theory partition functions in three dimensions

Abstract We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the e-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear σ -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 QCD 3 Dirac operator, as well as the corresponding massive spectral sum rules.