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

TL;DR

The paper develops two ${\rm BMS}_3$-invariant 2D field theories as flat-space limits of Liouville theory to model boundary dynamics of 3D gravity at null infinity. One limit yields a non-centrally extended theory, while the other produces a Centrally extended ${\rm bms}_3$ algebra with central charges matching gravitational surface-charge results, linking boundary dynamics to flat-space holography. By deriving the conserved charges, energy–momentum tensor, and Bäcklund-transformed general solutions for each limit, the work provides a concrete field-theoretic framework that parallels the AdS/CFT-Liouville correspondence in the flat setting. The approach paves the way for a Hamiltonian reduction from the CS formulation of 3D gravity to an explicit flat-limit boundary action, with potential implications for flat-space holography and gravitational entropy from symmetry arguments.

Abstract

In the gravitational context, Liouville theory is the two-dimensional conformal field theory that controls the boundary dynamics of asymptotically 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 BMS_3 invariant two-dimensional field theory that is likely to control the boundary dynamics at null infinity of three dimensional asymptotically flat gravity.