Brane nucleation instabilities in non-AdS/non-CFT

TL;DR

This paper explores how the weak gravity conjecture constrains the existence of disordered phases in holographic theories with broken supersymmetry and conformal invariance, revealing brane nucleation instabilities and metastable color superconducting states.

Contribution

It demonstrates that brane nucleation instabilities prevent disordered phases at zero temperature in certain holographic models with broken symmetries.

Findings

Disordered phase becomes unstable at low chemical potentials.

Metastable phases favor partial Higgsing of the gauge group.

Global minima outside the horizon indicate brane nucleation instabilities.

Abstract

We speculate that the weak gravity conjecture applied to theories with holographic duals bans the existence of disordered phases at zero temperature. We test this idea by introducing a non-zero baryon chemical potential in a deformation of the $SU(N_c)\times SU(N_c)$ Klebanov-Witten gauge theory with broken supersymmetry and conformal invariance. At low temperature, a disordered phase dual to a black brane geometry is unstable for low chemical potentials and metastable for high values. In the metastable phase, states with a partial Higgsing of the gauge group are favored over the normal disordered phase. This is reflected in the properties of the effective potential for color branes in the dual geometry, where the appearance of a global minimum outside the horizon signals the onset of a brane nucleation instability. When the Higgsing involves only one of the group factors, the global minimum remains at a finite distance from the horizon, making it possible to construct holographic duals to metastable "color superconducting" states. We also consider branes dual to excitations with baryon charge, but find that the extremal geometry remains marginally stable against the emission of particles carrying baryon charge independently of the strength of the deformation.