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Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry
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abstract
We prove that in $(3+1)d$ quantum field theories with $\mathbb{Z}_N$ symmetry, certain anomalies forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, this applies to discrete chiral symmetries which are frequently present in gauge theories as we illustrate in examples. Our results also constrain the long-distance behavior of certain condensed matter systems such as Weyl-semimetals and may have applications to crystallographic phases with symmetry protected topological order. These results may be viewed as analogs of the Lieb-Schultz-Mattis theorem for continuum field theories.
Forward citations
Cited by 6 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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Finite-group-enriched 3+1d topological orders are classified by 2SVect-enriched G-crossed braided fusion 2-categories, with gauging obstructions living in SW^5(BG).
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SymTFT, Protected Gaplessness, and Spontaneous Breaking of Non-invertible Symmetries
The authors classify, via Galois theory of cyclotomic polynomials, when finite duality symmetry groups of 4d BF-type SymTFTs admit invariant Lagrangian boundary conditions, thereby determining when symmetry-preserving...
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Fermion Families and Pontryagin Class: Topological Field Theory via Colour Symmetry Extension
From anomaly cancellation plus a stipulated minimality principle, the Standard Model is forced to N_c=N_f=3; the paper proves supporting theorems: H^d(Z_n,U(1)) cocycles split under the Z_n→Z_{n^2} extension, while A_...
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Anomalies imply vanishing brane partition functions; this yields unified derivations of the Freed-Witten and M5 shifted-quantization conditions and new S-fold D3-brane constraints.
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Explicit integer-valued anomaly indices for 4d Weyl fermions with Spin×Z_n and Spin×_{Z_2^F} Z_{2m} symmetries are derived from restriction of continuous U(1) anomalies and η-invariant evaluations.
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