Holographic Duals of Symmetry Broken Phases

Abstract

A novel interpretation of Symmetry Topological Field Theories (SymTFTs) as theories of gravity is explored by 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. The authors tested 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, many Abelian SymTFTs are found to be 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. The analysis is also extended to include the non-invertible $Q/Z$ axial symmetry, which is shown 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 $U\left(N\right)$ QCD.