Holographic duals of symmetry broken phases

TL;DR

This paper proposes a holographic duality linking Symmetry Topological Field Theories (SymTFTs) with effective field theories describing spontaneous symmetry breaking, supported by various examples across different symmetry structures.

Contribution

It introduces a new holographic interpretation of SymTFTs as dual to boundary EFTs of symmetry breaking, including non-Abelian, non-invertible, and higher group symmetries.

Findings

Abelian SymTFTs dual to free Goldstone or Maxwell fields

Non-Abelian SymTFTs relate to non-linear sigma models

Non-invertible $rac{Q}{Z}$ symmetry dual to axion-Maxwell theory

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.