Two-dimensional gravity with dynamical torsion and strings

Abstract

A two-dimensional theory of gravity with dynamical metric and torsion that was proposed in the context of string theory is considered. We analyse the equations of motion following from a Lagrangian quadratic in curvature and torsion, L = R 2 + T 2 + λ. The equations of motion are reduced to a system of equations for two scalar fields which in a particular case yields the Liouville equation. We have found and analysed stationary solutions with nontrivial torsion. It is proved that equations for extremals defining trajectories of pointlike spinless particles are completely integrable. A singularity of stationary space-time with nontrivial torsion has a repulsive character contrary to that of a black hole, and no particle can penetrate through it. Modification of the string theory due to the addition of the gravity Lagrangian is discussed.