Yang-Mills model for centrally extended 2D gravity

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