Anomaly matching in QCD thermal phase transition

Abstract

We study an 't Hooft anomaly of massless QCD at finite temperature. With the imaginary baryon chemical potential at the Roberge-Weiss point, there is a ${\mathbb{Z}}_2$ symmetry which can be used to define confinement. We show the existence of a mixed anomaly between the ${\mathbb{Z}}_2$ symmetry and the chiral symmetry, which gives a strong relation between confinement and chiral symmetry breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to three dimensions. It is reproduced in the chiral Lagrangian by a topological term related to Skyrmion charge, matching the anomaly before and after QCD phase transition. The effect of the imaginary chemical potential is suppresssed in the large $N$ expansion, and we discuss implications of the 't~Hooft anomaly matching for the nature of QCD phase transition with and without the imaginary chemical potential. Arguments based on universality alone are disfavored, and a first order phase transition may be the simplest possibility if the large $N$ expansion is qualitatively good.

arXiv comment41 pages, 5 figures. V2: references added

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• Cosmic strings from pure Yang-Mills theory
• Revisiting Wess-Zumino-Witten terms
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• General anomaly matching by Goldstone bosons
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
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• High-temperature domain walls of QCD with imaginary chemical potentials
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• Anomaly-induced transport phenomena from the imaginary-time formalism
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