Abstract
We show that there is a sector of quantum general relativity, in the Lorentzian signature case, which may be expressed in a completely holographic formulation in terms of states and operators defined on a finite boundary. The space of boundary states is built out of the conformal blocks of WZW field theory on the n-punctured sphere, where n is related to the area of the boundary. The Bekenstein bound is explicitly satisfied. These results are based on a new Lagrangian and Hamiltonian formulation of general relativity based on a constrained topological field theory. The Hamiltonian formalism is polynomial, and also left-right symmetric. The quantization uses balanced spin networks and so justifies the state sum model of Barrett and Crane. By extending the formalism to a holographic formulation of extended supergravity is obtained, as will be described in detail in a subsequent paper.
- Received 8 September 1998
DOI:https://doi.org/10.1103/PhysRevD.61.084007
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