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

Understand

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.