Compactified holographic conformal order

TL;DR

This paper investigates holographic conformal order on a compactified space, revealing a stable disordered phase and an unstable ordered phase with a hairy black hole dual, highlighting stability differences in holographic models.

Contribution

It demonstrates that compactification preserves the ordered phase but does not stabilize it, and shows the disordered phase remains perturbatively stable in Einstein-scalar holographic models.

Findings

Ordered phase persists under compactification but remains perturbatively unstable.

Disordered phase is perturbatively stable in the studied holographic models.

Hairy black hole duals violate the no-hair theorem, indicating complex gravitational structures.

Abstract

We study holographic conformal order compactified on $S^3$. The corresponding boundary CFT$ _4$ has a thermal phase with a nonzero expectation value of a certain operator. The gravitational dual to the ordered phase is represented by a black hole in asymptotically $AdS_5$ that violates the no-hair theorem. While the compactification does not destroy the ordered phase, it does not cure its perturbative instability: we identify the scalar channel QNM of the hairy black hole with Im$[w]>0$. On the contrary, we argue that the disordered thermal phase of the boundary CFT is perturbatively stable in holographic models of Einstein gravity and scalars.