Discrete scale invariance in holography revisited

TL;DR

This paper revisits a 2013 holographic model, analytically demonstrating that the full AdS_5 isometry group remains intact despite apparent symmetry breaking, and discusses future prospects for models with discrete scale invariance.

Contribution

It provides an analytical proof that the full AdS_5 isometry persists in a model previously thought to break it, clarifying the nature of discrete scale invariance in holography.

Findings

Full AdS_5 isometry group is preserved in the model

Analytical solution of Killing equations confirms hidden symmetries

Discussion on future holographic models with discrete scale invariance

Abstract

In 2013, Balasubramanian presented a 5+1 dimensional holographic toy model that allows for an exact solution to Einstein's equations in the bulk in which the isometries of $AdS_5$ appear to be broken to an isometry group describing a discretely scale invariant and Poincar\'e invariant setup [arXiv:1301.6653]. In this paper, we investigate this solution in more detail. By analytically solving the Killing equations, we prove that the full $AdS_5$ isometry group is still present, although in a somewhat hidden way. We will also comment on the prospects of finding other holographic bottom up toy models which allow for solutions with discrete scale invariance or scale invariance without conformal invariance in the future.