Three-dimensional asymptotically flat Einstein-Maxwell theory

TL;DR

This paper analyzes three-dimensional Einstein–Maxwell theory with nontrivial null infinity, revealing a Virasoro–Kac–Moody asymptotic symmetry that extends the purely gravitational bms3 algebra. It constructs a polyhomogeneous solution space featuring logarithmic terms and shows that the associated surface charges are non-integrable and non-conserved due to electromagnetic news, with a novel field-dependent central extension in the charge algebra. By switching off the news, charges become integrable and conserved while the symmetry algebra remains time-independent but still exhibits a field-dependent central term. The results illuminate parallels and differences with higher-dimensional cases and provide a tractable 3D setting to study algebroid structures and central extensions in gravitational and gauge theories.

Abstract

Three-dimensional Einstein-Maxwell theory with non trivial asymptotics at null infinity is solved. The symmetry algebra is a Virasoro-Kac-Moody type algebra that extends the bms3 algebra of the purely gravitational case. Solution space involves logarithms and provides a tractable example of a polyhomogeneous solution space. The associated surface charges are non-integrable and non-conserved due to the presence of electromagnetic news. As in the four dimensional purely gravitational case, their algebra involves a field-dependent central charge.