  We study the system of self-dual Maxwell field coupled to 3D gravity with
torsion, with Maxwell field modified by a topological mass term. General
structure of the field equations reveals a new, dynamical role of the classical
central charges, and gives a simple correspondence between self-dual solutions
with torsion and their Riemannian counterparts. We construct two exact
self-dual solutions, corresponding to the sectors with massless and massive
Maxwell field, and calculate their conserved charges.

General Relativity and Quantum Cosmology