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Theta, time reversal and temperature

Gaiotto, Davide and Kapustin, Anton and Komargodski, Zohar and Seiberg, Nathan (2017) Theta, time reversal and temperature. Journal of High Energy Physics, 2017 (5). Art. No. 091. ISSN 1029-8479. doi:10.1007/JHEP05(2017)091.

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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. It may also be that the four-dimensional theory around θ = π is gapless, e.g. a Coulomb phase could match the underlying anomalies.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Komargodski, Zohar0000-0002-8486-0811
Seiberg, Nathan0000-0003-3897-046X
Additional Information:© 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: March 31, 2017. Accepted: May 7, 2017. Published: May 17, 2017. We would like to thank O. Aharony, F. Benini, C. Cordova, M. Dine, J. Gomis, M.B. Green, T. Johnson-Freyd, M. Metlitski, A. Schwimmer, S. Shenker, and E. Witten for useful discussions, and especially Y. Tachikawa for collaboration at the early stage of this work. The work of D.G. was supported by the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. A.K. is supported by the Simons Investigator Award and in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 Z.K. is supported in part by an Israel Science Foundation center for excellence grant and by the I-CORE program of the Planning and Budgeting Committee and the Israel Science Foundation (grant number 1937/12). Z.K. is also supported by the ERC STG grant 335182 and by the United States-Israel BSF grant 2010/629. NS was supported in part by DOE grant DE-SC0009988. NS thanks the Hanna Visiting Professor Program and the Stanford Institute for Theoretical Physics for support and hospitality during the completion of this work.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Ontario Ministry of Economic Development and InnovationUNSPECIFIED
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Industry CanadaUNSPECIFIED
I-CORE Program of the Planning and Budgeting CommitteeUNSPECIFIED
Israel Science Foundation1937/12
European Research Council (ERC)335182
Binational Science Foundation (USA-Israel)2010/629
Department of Energy (DOE)DE-SC0009988
Stanford Institute for Theoretical PhysicsUNSPECIFIED
Subject Keywords:Anomalies in Field and String Theories Confinement Spontaneous Symmetry Breaking Wilson ’t Hooft and Polyakov loops
Issue or Number:5
Record Number:CaltechAUTHORS:20170607-094158330
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Official Citation:Gaiotto, D., Kapustin, A., Komargodski, Z. et al. J. High Energ. Phys. (2017) 2017: 91. doi:10.1007/JHEP05(2017)091
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77995
Deposited By: Ruth Sustaita
Deposited On:07 Jun 2017 18:20
Last Modified:15 Nov 2021 17:35

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