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arXiv · 1605.09618

Extrinsic curvature in 2-dimensional Causal Dynamical Triangulation

Lisa Glaser·Thomas P. Sotiriou·Silke Weinfurtner
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Abstract

Causal Dynamical Triangulations (CDT) is a non-perturbative quantisation of general relativity. Ho\v{r}ava-Lifshitz gravity on the other hand modifies general relativity to allow for perturbative quan- tisation. Past work has given rise to the speculation that Ho\v{r}ava-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 Ho\v{r}ava-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 Ho\v{r}ava-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.

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Lisa Glaser, Thomas P. Sotiriou, Silke Weinfurtner. 2016-05-31. Extrinsic curvature in 2-dimensional Causal Dynamical Triangulation. https://doi.org/10.1103/physrevd.94.064014

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