Abstract
We propose a model of quantum gravity in arbitrary dimensions defined in terms of the Batalin Vilkovisky (BV) quantization of a supersymmetric, infinite dimensional matrix model. This gives an Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ)-type Chern-Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert space . The model is motivated by previous attempts to formulate gravity in terms of noncommutative, phase space, field theories as well as the Fefferman-Graham (FG) curved analog of Dirac spaces for conformally invariant wave equations. The field equations are flat connection conditions amounting to zero curvature and parallel conditions on operators acting on . This matrix-type model may give a better defined setting for a quantum gravity path integral. We demonstrate that its underlying physics is a summation over Hamiltonians labeled by a conformal class of metrics and thus a sum over causal structures. This gives in turn a model summing over fluctuating metrics plus a tower of additional modes—we speculate that these could yield improved UV behavior.
- Received 13 August 2014
DOI:https://doi.org/10.1103/PhysRevD.90.084018
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