General analytic solution ofR2gravity with dynamical torsion in two dimensions

Using light-cone variables, we show that $R^2$ gravity with dynamical torsion in two dimensions is one of the rare field theories whose complete classical solution in closed form can be obtained. It fulfils an invariant relation between the cosmological constant, the curvature scalar, and the scalar formed by the torsion tensor. We conjecture that this relation, interpreted as a local conservation law, is closely connected to the integrability of the theory. The solutions may possess a rich spectrum of singularities in curvature and torsion. Special cases, including one with nonvanishing torsion, can be used to elucidate some physical properties of the solution where by "physical" we imply the validity of concepts from general relativity such as measurements of distances and times and of extremal trajectories of a scalar test particle.