SUGRA/Strings like to be bald

TL;DR

This paper investigates the embedding of holographic models with ordered conformal phases into string theory, revealing that such models may not be consistent within the string theory landscape due to their disappearance under certain deformations.

Contribution

It introduces a phenomenological deformation parameter in the scalar potential to study ordered phases and shows these phases vanish before the deformation is removed, suggesting they are in the swampland.

Findings

Ordered phases exist for various deformation parameters.

Ordered phases disappear before the potential matches top-down holography.

Models with ordered phases may be in the string theory swampland.

Abstract

We explore the embedding of the phenomenological holographic models describing thermal relativistic ordered conformal phases in ${\mathbb R}^{2,1}$ in SUGRA/String theory. The dual black branes in a Poincare patch of asymptotically $AdS_4$ have ``hair'' -- a condensate of the order parameter for the broken symmetry. In a gravitational dual the order parameter for a spontaneous symmetry breaking is represented by a bulk scalar field with a nontrivial potential. To construct the ordered conformal phases perturbatively we introduce a phenomenological deformation parameter in the scalar potential. We find that while the ordered phases exist for different values of the deformation parameter, they disappear before the deformation is removed, in one case once the potential is precisely as in the top-down holography. It appears that the holographic models with the conformal ordered phases are in the String theory swampland.