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Constraints on Symmetry Preserving Gapped Phases from Coupling Constant Anomalies
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abstract
In this note, we will characterize constraints on the possible IR phases of a given QFT by anomalies in the space of coupling constants. We will give conditions under which a coupling constant anomaly cannot be matched by a continuous family of symmetry preserving gapped phases, in which case the theory is either gapless, or exhibits spontaneous symmetry breaking or a phase transition. We additionally demonstrate examples of theories with 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."
Forward citations
Cited by 3 Pith papers
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Generalized Families of QFTs
Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
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Tilts from 2-Groups
Line operators charged under the 1-form part of a 2-group symmetry must generically break the 0-form part, enforced by a family anomaly derived from Wess-Zumino consistency.
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Notes on (-2)-form symmetries
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...
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