  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.
