Super-BMS$_{3}$ invariant boundary theory from three-dimensional flat supergravity

TL;DR

The paper constructs a 2D super-BMS3 invariant theory dual to 3D asymptotically flat N=1 supergravity via three equivalent formulations: a constrained chiral WZW model based on the super-Poincaré algebra, a gauged chiral WZW model, and a reduced supersymmetric flat Liouville-like theory. It shows how solving boundary constraints yields a boundary chiral WZW action with explicit currents that realize an affine super-Poincaré algebra, and how a modified Sugawara construction produces the centrally extended super-BMS3 algebra after imposing first-class constraints. The work identifies the central charges c1 = 3μ/G and c2 = 3/G and provides consistent reductions to a supersymmetric flat Liouville theory, maintaining super-BMS3 invariance throughout. An equivalent gauged-WZW description is also developed, linking the constrained and reduced pictures and illustrating the role of boundary conditions in shaping the 2D dual theory.

Abstract

The two-dimensional super-BMS$_{3}$ invariant theory dual to three-dimensional asymptotically flat $\mathcal{N}=1$ supergravity is constructed. It is described by a constrained or gauged chiral Wess-Zumino-Witten action based on the super-Poincaré algebra in the Hamiltonian, respectively the Lagrangian formulation, whose reduced phase space description corresponds to a supersymmetric extension of flat Liouville theory.