Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields

TL;DR

The paper constructs a two dimensional action invariant under a spin-3 extension of the $bms_3$ symmetry by reducing a Chern-Simons formulation of 3D gravity with boundary. It derives a flat WZW model based on a contraction of $sl(3,\mathbb{R})$, builds currents and an extended Sugawara construction to realize a spin-3 extension of $bms_3$, and implements boundary constraints to obtain a reduced action whose Dirac brackets reproduce the central extended algebra. A key result is that a sector of the reduced theory matches the flat limit of $sl(3,\mathbb{R})$ Toda theory, establishing a link between flat space holography, higher spin gravity, and integrable structures. The work also outlines generalizations to higher rank groups and discusses implications for holography in asymptotically flat spacetimes and potential quantum extensions.

Abstract

We construct a two-dimensional action principle invariant under a spin-three extension of BMS$_3$ group. Such a theory is obtained through a reduction of Chern-Simons action with a boundary. This procedure is carried out by imposing a set of boundary conditions obtained from asymptotically flat spacetimes in three dimensions. When implementing part of this set, we obtain an analog of chiral WZW model based on a contraction of $sl(3,\mathbb{R}) \times sl(3,\mathbb{R})$. The remaining part of the boundary conditions imposes constraints on the conserved currents of the model, which allows to further reduce the action principle. It is shown that a sector of this latter theory is related to a flat limit of Toda theory.