Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory

Abstract

In the gravitational context, Liouville theory is the two-dimensional conformal field theory that controls the boundary dynamics of asymptotically ${\mathrm{AdS}}_{3}$ spacetimes at the classical level. By taking a suitable limit of the coupling constants of the Hamiltonian formulation of Liouville, we construct and analyze a ${\mathrm{BMS}}_{3}$ invariant two-dimensional field theory that is likely to control the boundary dynamics at null infinity of threedimensional asymptotically flat gravity.