Consistency Conditions for Finite-Volume Partition Functions

TL;DR

This paper derives exact spectral correlation functions for Dirac operator eigenvalues in finite-volume gauge theories using random matrix theory, establishing new consistency conditions for partition functions in different symmetry classes.

Contribution

It provides explicit formulas for spectral correlations and introduces an infinite sequence of consistency conditions for finite-volume partition functions in chiral random matrix ensembles.

Findings

Exact expressions for spectral correlation functions derived

Consistency conditions for partition functions established

Applicable to theories with different gauge and fermion representations

Abstract

Using relations from random matrix theory, we derive exact expressions for all $n$-point spectral correlation functions of Dirac operator eigenvalues in terms of finite-volume partition functions. This is done for both chiral symplectic and chiral unitary random matrix ensembles, which correspond to $SU(N_c \geq 3)$ gauge theories with $N_f$ fermions in the adjoint and fundamental representations, respectively. In the latter case we infer from this an infinite sequence of consistency conditions that must be satisfied by the corresponding finite-volume partition functions.