Gauge Invariance and Holographic Renormalization

TL;DR

This paper explores how gauge invariance in holographic theories is maintained through holographic renormalization, revealing a residual gauge symmetry that resolves degrees of freedom mismatch.

Contribution

It identifies the role of residual gauge symmetry in holographic renormalization and extends it to satisfy boundary conditions, clarifying gauge invariance in holographic setups.

Findings

Holographic renormalization cancels gauge dependences and divergences.

Residual gauge symmetry explains degrees of freedom mismatch.

Extending residual gauge symmetry to horizon conditions clarifies gauge invariance.

Abstract

We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalisation: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry(RGS). By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.