Holography of Broken U(1) Symmetry

TL;DR

This paper explores the holographic dual of a broken U(1) symmetry in an AdS setup with a bulk Higgs, revealing how the gauge spectrum and dual CFT current dimensions depend on the Higgs mass and symmetry breaking.

Contribution

It introduces two Goldstone boson equivalence theorems for boundary and bulk, and analyzes the gauge spectrum and current anomalous dimensions in the holographic model.

Findings

The gauge spectrum can be a continuum, gapped continuum, or discretuum.

The dual CFT has a non-conserved U(1) current with anomalous dimension related to the Higgs VEV.

The U(1) current dimension runs logarithmically with energy when the Higgs weakly breaks AdS isometries.

Abstract

We examine the Abelian Higgs model in (d+1)-dimensional anti-de Sitter space with an ultraviolet brane. The gauge symmetry is broken by a bulk Higgs vacuum expectation value triggered on the brane. We propose two separate Goldstone boson equivalence theorems for the boundary and bulk degrees of freedom. We compute the holographic self-energy of the gauge field and show that its spectrum is either a continuum, gapped continuum, or a discretuum as a function of the Higgs bulk mass. When the Higgs has no bulk mass, the AdS isometries are unbroken. We find in that case that the dual CFT has a non-conserved U(1) current whose anomalous dimension is proportional to the square of the Higgs vacuum expectation value. When the Higgs background weakly breaks the AdS isometries, we present an adapted WKB method to solve the gauge field equations. We show that the U(1) current dimension runs logarithmically with the energy scale in accordance with a nearly-marginal U(1)-breaking deformation of the CFT.