Self-dual Maxwell field in 3D gravity with torsion

TL;DR

This paper explores self-dual Maxwell fields coupled with 3D gravity with torsion, revealing new roles for classical central charges and providing exact solutions with conserved charges.

Contribution

It introduces a novel analysis of self-dual Maxwell fields in 3D gravity with torsion, highlighting the role of central charges and constructing explicit solutions.

Findings

Identified a new dynamical role of classical central charges.

Constructed exact self-dual solutions with massless and massive Maxwell fields.

Calculated conserved charges for the solutions.

Abstract

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.