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

Abstract

We derive exact analytical expressions for the spectral density of the Dirac operator at fixed θ-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.

arXiv comment12 pages, 6 figures

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Cited by in corpus (10)

• Vacuum structure of bifundamental gauge theories at finite topological angles
• The Dirac spectrum in Complex Langevin Simulations of QCD
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• Ordinary and exotic mesons in the extended Linear Sigma Model
• Spectral density of the Dirac-Ginsparg-Wilson operator, chiral $U(1{)}_A$ anomaly, and analyticity in the high temperature phase of $QCD$
• Random matrix approach to three-dimensional QCD with a Chern-Simons term
• Absence of $CP$ violation in the strong interactions
• Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfluids
• Dirac spectrum and chiral condensate for QCD at fixed $\theta$-angle
• First-order CP phase transition in two-flavor QCD at $\theta =\pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description