Dirac spectrum of one-flavor QCD at \theta=0 and continuity of the chiral condensate

TL;DR

This paper derives exact formulas for the Dirac spectral density in one-flavor QCD at zero theta, revealing how the chiral condensate remains continuous despite the non-positivity of the fermion determinant.

Contribution

It provides novel analytical expressions for the spectral density using new identities, and explains the continuity of the chiral condensate across zero quark mass.

Findings

Exact spectral density formulas for one-flavor QCD at =0

Demonstration of chiral condensate continuity across mass sign change

Identification of a non-standard mechanism replacing Banks-Casher relation

Abstract

We derive exact analytical expressions for the spectral density of the Dirac operator at fixed \theta-angle in the microscopic domain of one-flavor QCD. These results are obtained by performing the sum over topological sectors using novel identities involving sums of products of Bessel functions. Because the fermion determinant is not positive definite for negative quark mass, the usual Banks-Casher relation is not valid and has to be replaced by a different mechanism first observed for QCD at nonzero chemical potential. Using the exact results for the spectral density we explain how this mechanism results in a chiral condensate that remains constant when the quark mass changes sign.