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Obstructions to Gapped Phases from Non-Invertible Symmetries

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arxiv 2212.14605 v1 pith:G3Q5BFD2 submitted 2022-12-30 hep-th cond-mat.str-el

classification hep-thcond-mat.str-el
keywords symmetriesnon-invertiblesymmetrydefectsdualitygappedgaugingone-form
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abstract

Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, we prove that a self-dual theory with $\mathbb{Z}_{N}^{(1)}$ one-form symmetry is gapless or spontaneously breaks the self-duality symmetry unless $N=k^{2}\ell$ where $-1$ is a quadratic residue modulo $\ell$. We also extend these results to non-invertible symmetries arising from invariance under more general gauging operations including e.g. triality symmetries. Along the way, we discover how duality defects in symmetry protected topological phases have a hidden time-reversal symmetry that organizes their basic properties. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Generalized Families of QFTs

    hep-th 2026-02 unverdicted novelty 7.0 of 10

    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.

  2. SymTFT Approach for Mixed States with Non-Invertible Symmetries

    quant-ph 2025-07 conditional novelty 7.0 of 10

    A SymTFT-based classification of 1+1d mixed-state phases with non-invertible strong and weak symmetries, with explicit lattice-model examples.

  3. Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations

    quant-ph 2026-07 conditional novelty 6.0 of 10

    Gravitational topological responses are shown to appear as the projective phase (ST)^3=Y in gauging/stacking relations, corresponding on the lattice to nontrivial QCAs implementable via finite-depth circuits, measurem...

  4. The Higher Structure of Symmetries of Axion-Maxwell Theory

    hep-th 2024-11 conditional novelty 6.0 of 10

    The paper determines the fusion interfaces and F-symbols for the non-invertible electric 1-form symmetry of 4d axion-Maxwell theory.

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