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Title: Theta, time reversal and temperature

SU(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 leads to constraints on the vacua of the theory. It follows that at θ = π the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at θ = 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 θ = π, 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 θ = π is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two O(2)-symmetric fixed points. In conclusion, it may also be that the four-dimensional theory around θ = π is gapless, e.g. a Coulomb phase could match the underlying anomalies.
 [1] ;  [2] ;  [3] ;  [4]
  1. Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States)
  3. Weizmann Institute of Science, Rehovot (Israel)
  4. Institute for Advanced Study, Princeton, NJ (United States)
Publication Date:
Grant/Contract Number:
SC0011632; SC0009988
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 5; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
California Institute of Technology, Pasadena, CA (United States), Institute for Advanced Study
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories; Confinement; Spontaneous Symmetry Breaking; Wilson; ’t Hooft and Polyakov loops
OSTI Identifier: