Three-dimensional asymptotically flat Einstein–Maxwell theory

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. (paper)