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Constraints on symmetry-preserving gapped phases from coupling constant anomalies

Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0319, USA

Phys. Rev. D 110, L041701 – Published 14 August, 2024

DOI: https://doi.org/10.1103/PhysRevD.110.L041701

Abstract

We characterize constraints on the possible IR phases of quantum field theories from coupling constant anomalies. We give conditions for when a coupling constant anomaly cannot be matched by a continuous family of symmetry preserving gapped phases: the theory must then be gapless or exhibit spontaneous symmetry breaking or a phase transition. We demonstrate examples of coupling constant anomalies which can be matched by a family of symmetry preserving gapped phases without a phase transition and comment on the interpretation of our results for the spontaneous breaking of “( $- 1$ )-form global symmetries.”

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Here, $B G$ is the classifying space for the symmetry group $G = G^{(p - 1)} \times G^{(d - p - 1)}$ which is given by: $B G ≔ B^{p} G^{(p - 1)} \times B^{d - p} G^{(d - p - 1)}$ .
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Here we will only focus on $Z_{N}^{(1)}$ background for which $B_{2} \in H^{2} (X_{d}; Z_{N})$ has an integral lift. In general, the fractional part of Chern characters can different when $B_{2}$ does not have an integer lift.
Note that alternatively, the phase proportional to ${\hat{c}}_{2}$ for $6 d$ Yang-Mills and the terms ${\hat{c}}_{2, 3}$ for $8 d$ Yang-Mills can be additionally removed by turning on backgrounds for the $U (1)^{(1)}$ and $U (1)^{(1)} \times U (1)^{(3)}$ respectively.

Phys. Rev. D 110, L041701– Published 14 August, 2024

Vol. 110, Iss. 4 — 15 August 2024

Received 10 May 2024
Accepted 26 July 2024

DOI: https://doi.org/10.1103/PhysRevD.110.L041701

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Constraints on symmetry-preserving gapped phases from coupling constant anomalies

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