Geometric actions and flat space holography

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 BMS3 coad- joint 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 BMS3 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. We use the expectation values and two-point correlation functions of these bilocal operators to compute quantum contributions to the entanglement entropy of a single interval for BMS3 invariant field theories and BMS3 blocks, respectively. While semi-classically the BMS3 boundary theory has central charges c(1) = 0 and c(2) = 3/G(N), we find that quantum corrections in flat space do not renormalize G(N), but rather lead to a non-zero c(1).