Extrinsic curvature in two-dimensional causal dynamical triangulation

Glaser, Lisa; Sotiriou, Thomas P.; Weinfurtner, Silke

Abstract

Causal dynamical triangulation (CDT) is a nonperturbative quantization of general relativity. Hořava-Lifshitz gravity, on the other hand, modifies general relativity to allow for perturbative quantization. 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 quantization prescription directly to Hořava-Lifshitz gravity in two dimensions. We derive the continuum Hamiltonian, and we show that it matches exactly the Hamiltonian derived from canonically quantizing the Hořava-Lifshitz action. Unlike the standard CDT case, here the introduction of a foliated lattice does not impose further restriction on the configuration space and, as a result, lattice quantization does not leave any imprint on continuum physics as expected.

Citation

Glaser, L., Sotiriou, T. P., & Weinfurtner, S. (2016). Extrinsic curvature in two-dimensional causal dynamical triangulation. Physical Review D, 94(6), Article 64014. https://doi.org/10.1103/PhysRevD.94.064014

• Journal Article Type: Article
• Acceptance Date: Aug 31, 2016
• Publication Date: Sep 7, 2016
• Deposit Date: Dec 21, 2016
• Publicly Available Date: Dec 21, 2016
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 94
• Issue: 6
• Article Number: 64014
• DOI: https://doi.org/10.1103/PhysRevD.94.064014
• Public URL: https://nottingham-repository.worktribe.com/output/818707
• Publisher URL: http://dx.doi.org/10.1103/PhysRevD.94.064014
• Additional Information: ©2016 American Physical Society
• Contract Date: Dec 21, 2016