# Chiral condensate and Dirac spectrum of one- and two-flavor QCD at nonzero $θ$-angle

@inproceedings{Kieburg2018ChiralCA,
title={Chiral condensate and Dirac spectrum of one- and two-flavor QCD at nonzero \\theta$\$-angle},
author={Mario Kieburg and Jacobus J. M. Verbaarschot and Tilo Wettig},
year={2018}
}
• Published 18 October 2017
• Physics
In previous work we showed that the chiral condensate of one-flavor QCD exhibits a Silver Blaze phenomenon when the quark mass crosses m = 0: the chiral condensate remains constant while the quark mass crosses the spectrum of the Dirac operator, which is dense on the imaginary axis. This behavior can be explained in terms of exponentially large cancellations between contributions from the zero modes and from the nonzero modes when the quark mass is negative. In these proceedings we show that a…
3 Citations

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## References

SHOWING 1-10 OF 35 REFERENCES

### Dirac spectrum and chiral condensate for QCD at fixed θ angle

• Physics
Physical Review D
• 2019
We analyze the mass dependence of the chiral condensate for QCD at nonzero $\theta$-angle and find that in general the discontinuity of the chiral condensate is not on the support of the Dirac

### Pion masses in two-flavor QCD with η condensation.

• Physics
Physical review letters
• 2014
It is shown that the "topological susceptibility" in the chiral perturbation theory diverges at these two critical points of mu, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase.

### Singular values of the Dirac operator in dense QCD-like theories

• Mathematics, Physics
• 2011
A bstractWe study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale

### Chiral symmetry breaking and the dirac spectrum at nonzero chemical potential.

• Physics
Physical review letters
• 2005
The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated and it is found that the discontinuity of the chirus is due to the whole oscillating region rather than to an accumulation of eigenvalues at the origin.

### RANDOM MATRIX THEORY AND CHIRAL SYMMETRY IN QCD

• Physics
• 2000
▪ Abstract Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this

### Functional integrals for QCD at nonzero chemical potential and zero density.

• T. Cohen
• Physics
Physical review letters
• 2003
The problem of how to understand this phenomenological behavior in terms of functional integrals is solved for the case of an isospin chemical through the study of the spectrum of the operator gamma(0)(/D+m).

### Spectrum of the QCD Dirac operator and chiral random matrix theory.

It is argued that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory and reproduces Leutwyler-Smilga sum rules.

### Theta, time reversal and temperature

• Physics
• 2017
A bstractSU(N ) gauge theory is time reversal invariant at θ = 0 and θ = π. We show that at θ = π there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly