AdS Phase Transitions at finite \kappa

TL;DR

This paper explores how adding a Chern-Simons term and axion field to SU(2) Einstein-Yang-Mills theory in AdS space induces phase transitions between different black hole solutions, revealing new holographic superconducting phases.

Contribution

It introduces a novel holographic model with a Chern-Simons term and axion dynamics, demonstrating phase transitions and critical behavior in AdS black holes.

Findings

Phase transition between Reissner-Nordstrom and non-abelian condensate black holes.

Shifted critical temperature with axion mass and new order parameter scaling.

Observation of a superconducting phase with non-trivial axion profile.

Abstract

We investigate the effect of adding a Chern-Simons term coupled to an axion field to SU(2) Einstein-Yang-Mills in a fixed $AdS_4$/Schwarzschild background. We show that, when the axion has no potential, there is a phase transition between a Reissner-Nordstrom black-hole and one with a non-abelian condensate as per the vanishing Chern-Simons case. Furthermore, by giving the axion field a mass, one observes a phase transition between a Reissner-Nordstrom black-hole with axion hair to a "superconducting" phase which also has a non-trivial axion profile. We are able to perform a preliminary analysis for this interesting case and observe that we can shift the critical temperature at which the phase transition occurs and observe interesting features of the order parameter scaling form.