Strong coupling effective Higgs potential and a first order thermal phase transition from AdS/CFT duality

TL;DR

This paper investigates the thermodynamics and phase transitions of a strongly coupled supersymmetric gauge theory using AdS/CFT duality, revealing a first order transition and instabilities related to Bose-Einstein condensation.

Contribution

It demonstrates how the Higgs potential and phase structure can be analyzed via AdS/CFT, including the effects of temperature and chemical potential on the Higgs branch.

Findings

Identifies a first order phase transition at critical temperature Tc.

Shows the Higgs VEV as an order parameter for the transition.

Discovers instabilities at zero temperature with non-zero chemical potential.

Abstract

We use AdS/CFT duality to study the thermodynamics of a strongly coupled N=2 supersymmetric large Nc SU(Nc) gauge theory with Nf =2 fundamental hypermultiplets. At finite temperature T and isospin chemical potential mu, a potential on the Higgs branch is generated, corresponding to a potential on the moduli space of instantons in the AdS description. For mu =0, there is a known first order phase transition around a critical temperature Tc. We find that the Higgs VEV is a suitable order parameter for this transition; for T>Tc, the theory is driven to a non-trivial point on the Higgs branch. For non-zero mu and T=0, the Higgs potential is unbounded from below, leading to an instability of the field theory due to Bose-Einstein condensation.