A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography

TL;DR

This paper presents new analytic solutions in a holographic model linking topological gauge fields with thermodynamics, revealing insights into phase transitions and topological effects in strongly coupled systems like QCD and condensed matter.

Contribution

It introduces analytically known black hole and brane solutions with non-Abelian gauge fields and topological charges in Einstein-Skyrme holography, connecting topological properties to thermodynamics.

Findings

Chern numbers affect the Hawking-Page transition temperature.

Black holes with different Chern numbers can have the same temperature, enabling topological transitions.

Rotating solutions induce charge density waves in the dual field theory.

Abstract

We report analytically known states at non-zero temperature which may serve as a powerful tool to reveal common topological and thermodynamic properties of systems ranging from the QCD phase diagram to topological phase transitions in condensed matter materials. In the holographically dual gravity theory, these are analytic solutions to a five-dimensional non-linear-sigma (Skyrme) model dynamically coupled to Einstein gravity. This theory is shown to be holographically dual to $\mathcal{N}=4$ Super-Yang-Mills theory coupled to an $SU(2)$-current. All solutions are fully backreacted asymptotically Anti-de Sitter~(AdS) black branes or holes. One family of global AdS black hole solutions contains non-Abelian gauge field configurations with positive integer Chern numbers and finite energy density. Larger Chern numbers increase the Hawking-Page transition temperature. In the holographically dual field theory this indicates a significant effect on the deconfinement phase transition. Black holes with one Hawking temperature can have distinct Chern numbers, potentially enabling topological transitions. A second family of analytic solutions, rotating black branes, is also provided. These rotating solutions induce states with propagating charge density waves in the dual field theory. We compute the Hawking temperature, entropy density, angular velocity and free energy for these black holes/branes. These correspond to thermodynamic data in the dual field theory. For these states the energy-momentum tensor, (non-)conserved current, and topological charge are interpreted.