Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group

TL;DR

This paper demonstrates a dual interpretation of a 3D Manin gauge theory with SL(2,R) gauge group as Einstein gravity coupled to a gauge theory, introducing an 'ersatz' metric that allows black-hole thermodynamics to be formulated in this dual framework.

Contribution

It introduces a novel duality where a gauge theory with SL(2,R) gauge group is reinterpreted as Einstein gravity with an exchanged role of geometric and gauge fields, leading to a new perspective on black-hole thermodynamics.

Findings

The ersatz metric is a classical double copy of the gauge field strength.

Black-hole solutions in the ersatz metric obey thermodynamic laws.

Ersatz Hawking radiation can be derived from Yang-Mills fields.

Abstract

We show that a three-dimensional Manin gauge theory with gauge group $\operatorname{SL}(2;\mathbb R)$ (i.e. Yang-Mills theory, the third-way theory, or the imaginary third-way theory) minimally coupled to Einstein gravity admits a dual interpretation as Einstein gravity with an exotic coupling to a Manin gauge theory, where the roles of dreibein/spin connection and field strength/gauge potential are interchanged. The dual, or ersatz, gravitational metric $\hat g_{\mu\nu}\sim\operatorname{tr}((\star F)_\mu (\star F)_\nu)$ is a classical double copy of the gauge field strength $F_{\mu\nu}$ (as opposed to the usual double copy of the gauge potential $A_\mu$). If matter exclusively couples to $\hat g$ (for example, in a gravitational decoupling limit), then one can formulate black-hole thermodynamics with regards to the ersatz metric. In particular, a black-hole solution for the ersatz metric $\hat g_{\mu\nu}$ (made of Yang-Mills fields) radiates ersatz Hawking radiation and obeys the laws of black-hole thermodynamics.