Geometric actions and flat space holography

Understand

In this paper we perform the Hamiltonian reduction of the action for three-dimensional Einstein gravity with vanishing cosmological constant using the Chern-Simons formulation and Bondi-van der Burg-Metzner-Sachs (BMS) boundary conditions.

• An equivalent formulation of the boundary action is the geometric action on BMS$_3$ coadjoint orbits, where the orbit representative is identified as the bulk holonomy.
• We use this reduced action to compute one-loop contributions to the torus partition function of all BMS$_3$ descendants of Minkowski spacetime and cosmological solutions in flat space.
• We then consider Wilson lines in the ISO$(2,1)$ Chern-Simons theory with endpoints on the boundary, whose reduction to the boundary theory gives a bilocal operator.