Self-dual Maxwell field in 3D gravity with torsion and dynamical role of central charges

Abstract

We show that general structure of the field equations for the system of a self-dual Maxwell field coupled to 3D gravity with torsion implies that classical central charges have a new dynamical role. By using simple correspondence between self-dual solutions with torsion and their Riemannian counterparts we construct two exact solutions, corresponding to the sectors with a massless and massive Maxwell field, and calculate their conserved charges.