Theta, time reversal and temperature

DOI10.1007/JHEP05(2017)091zbMATH Open1380.83255arXiv1703.00501MaRDI QIDQ682981

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Publication date: 5 February 2018

Published in: (Search for Journal in Brave)

Abstract: $SU(N)$ gauge theory is time reversal invariant at $heta=0$ and $heta=pi$. We show that at $heta=pi$ there is a discrete 't Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at $heta=pi$ the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at $heta=0$ is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at $heta=pi$, several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for $SU(2)$ gauge theory. The underlying symmetry at $heta=pi$ is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two $O(2)$-symmetric fixed points. It may also be that the four-dimensional theory around $heta=pi$ is gapless, e.g. a Coulomb phase could match the underlying anomalies.

Full work available at URL: https://arxiv.org/abs/1703.00501

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