Holographic duals of symmetry broken phases

Abstract

We explore a novel interpretation of Symmetry Topological Field Theories (SymTFTs) as theories of gravity, proposing a holographic duality where the bulk SymTFT (with the gauging of a suitable Lagrangian algebra) is dual to the universal effective field theory (EFT) that describes spontaneous symmetry breaking on the boundary. We test this conjecture in various dimensions and with many examples involving different continuous symmetry structures, including non-Abelian and non-invertible symmetries, as well as higher groups. For instance, we find that many Abelian SymTFTs are dual to free theories of Goldstone bosons or generalized Maxwell fields, while non-Abelian SymTFTs relate to non-linear sigma models with target spaces defined by the symmetry groups. We also extend our analysis to include the non-invertible $\mathbb{Q}/\mathbb{Z}$ axial symmetry, finding it to be dual to axion-Maxwell theory, and a non-Abelian 2-group structure in four dimensions, deriving a new parity-violating interaction that has implications for the low-energy dynamics of U(N) QCD.

35 pages + appendices; v2: typos corrected and refs added, published version; v3: refs added

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• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT
• Symmetry Transmutation and Anomaly Matching
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• Non-Invertible $SO(2)$ Symmetry of 4d Maxwell from Continuous Gaugings
• Enhancement of quantum sensing in a dissipatively coupled two-mode system
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory
• Higher-form anomalies and state-operator correspondence beyond conformal invariance