Extrinsic curvature in 2-dimensional Causal Dynamical Triangulation

Abstract

Causal Dynamical Triangulations (CDT) is a non-perturbative quantisation of general relativity. Hořava-Lifshitz gravity on the other hand modifies general relativity to allow for perturbative quan- tisation. Past work has given rise to the speculation that Hořava-Lifshitz gravity might correspond to the continuum limit of CDT. In this paper we add another piece to this puzzle by applying the CDT quantisation prescription directly to Hořava-Lifshitz gravity in 2 dimensions. We derive the continuum Hamiltonian and we show that it matches exactly the Hamiltonian one derives from canonically quantising the Hořava-Lifshitz action. Unlike the standard CDT case, here the intro- duction of a foliated lattice does not impose further restriction on the configuration space and, as a result, lattice quantisation does not leave any imprint on continuum physics as expected.

9 pages, 3 figures (version 2 equivalent to published version)

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Cited by in corpus (4)

• Infinite order quantum-gravitational correlations
• The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
• The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations
• CDT and Horava-Lifshitz QG in Two Dimensions