Abstract
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 c1 = 0 and c2 = 3/GN, we find that quantum corrections in flat space do not renormalize GN, but rather lead to a non-zero c1.
Highlights
The holographic principle [1, 2] plays a vital role in our current understanding of quantum gravity
An equivalent formulation of the boundary action is the geometric action on BMS3 coadjoint orbits, where the orbit representative is identified as the bulk holonomy
We have performed the Hamiltonian reduction of the classical gravity action in Chern-Simons form and obtained exactly the geometric action on the coadjoint orbits of the BMS3 group of [62]
Summary
The holographic principle [1, 2] plays a vital role in our current understanding of quantum gravity. The relation between the Alekseev-Shatashvili (AS) action, quantization of the coadjoint orbits and three-dimensional gravity follows from ingredients that have been known in the literature for around thirty years [53, 61] and has been revived and expanded upon recently for flat spacetimes [62], AdS3 [63] and dS3 [64], see [65,66,67,68] It was noted in [60] that the AS action can be obtained as a Drinfeld-Sokolov reduction of the sl(2, R) WZW model, which is the CFT counterpart of choosing Brown-Henneaux boundary conditions.
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