Topology of black hole phase transition in JT gravity

TL;DR

This paper investigates the topology of black hole phase transitions in JT gravity coupled with Yang-Mills fields, identifying topological defects in thermodynamic space and analyzing their robustness and dual boundary theories.

Contribution

It introduces a novel topological framework for understanding black hole phase transitions in JT gravity with gauge fields, including calculations of topological numbers and perturbative corrections.

Findings

Black hole phase transition characterized as topological defects.

Topological numbers confirm the robustness of the phase transition.

Constructed boundary Schwarzian theory and discussed dual SYK-like models.

Abstract

We present a JT gravity setup coupled with $U(1)$ and $SU(2)$ Yang-Mills fields in two dimensions that reveals the onset of a small black hole to large black hole phase transition at finite chemical potential(s). We identify these black hole solutions as topological defects in the thermodynamic phase space and calculate the associated topological numbers following the standard procedure. We confirm the robustness of our model by estimating perturbative corrections to the bulk free energy at an arbitrary order in the Yang-Mills coupling. We also construct the Schwarzian for the boundary theory using the 2D gravitational action in the bulk and comment on the dual SYK like model where similar observations can be made.