Constraints on symmetry-preserving gapped phases from coupling constant anomalies

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 “(<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo>−</a:mo><a:mn>1</a:mn></a:math>)-form global symmetries.” Published by the American Physical Society 2024