Yang-Mills model for centrally extended 2d gravity

TL;DR

This paper formulates a Yang-Mills theory for 2d gravity with a specific symmetry structure, revealing solutions like black holes and constant curvature spaces, and establishing a conformal field theory interpretation related to known models.

Contribution

It introduces a novel Yang-Mills model for 2d gravity with a unique symmetry algebra, connecting it to existing theories and analyzing its solutions and boundary symmetries.

Findings

All vacuum solutions identified, including black holes and constant scalar curvature spaces.

Model exhibits a conformal field theory interpretation with residual symmetries.

Existence of solutions with zero cosmological constant but nonzero scalar curvature.

Abstract

A Yang-Mills theory linear in the scalar curvature for 2d gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As compared with dilaton models, the role of the dilaton is played by the dual field strength of a $U(1)$ gauge field. All vacuum solutions are found. They are either black holes or have constant scalar curvature. Those with constant scalar curvature have constant dual field strength. In particular, solutions with vanishing cosmological constant but nonzero scalar curvature exist. In the conformal-Lorenz gauge, the model has a CFT interpretation whose residual symmetry combines holomorphic diffeomorphisms with a subclass of U(1) gauge transformations while preserving dS2 and AdS2 boundary conditions. This is the same symmetry as in Jackiw-Teitelboim-Maxwell gravity considered by Hartman and Strominger. It is argued that this is the only nontrivial Yang-Mills model linear in the scalar curvature that exists for real Lie algebras of dimension four.