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Holographic duals of symmetry broken phases
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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.
Forward citations
Cited by 4 Pith papers
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Symmetry TFTs for Continuous Spacetime Symmetries
Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.
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Continuous symmetries and charge measurement of boundary operators in holography
Continuous symmetry operators in holography are U-shaped hanging brane bound states (D5-KK in Type IIB, M5-KK in M-theory) whose worldvolume couplings reproduce the Gauss-law symmetry operators and measure charges of ...
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SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking
Continuous-symmetry SymTFTs are extended to non-linear coset realizations and to spontaneous breaking using boundary and corner constructions, recovering CCWZ actions and SSB Ward identities.
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Topological Holography for Mixed-State Phases and Phase Transitions
Mixed-state phases of (1+1)D systems with finite group symmetry are classified by condensable algebras in the doubled topological order Z(Vec_{GxG}) subject to Hermiticity and positivity constraints.
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