Quantizing Hořava-Lifshitz gravity via causal dynamical triangulations

Abstract

We extend the discrete Regge action of causal dynamical triangulations to include discrete versions of the curvature squared terms appearing in the continuum action of (2+1)-dimensional projectable Hořava-Lifshitz gravity. Focusing on an ensemble of spacetimes whose spacelike hypersurfaces are 2-spheres, we employ Markov chain Monte Carlo simulations to study the path integral defined by this extended discrete action. We demonstrate the existence of known and novel macroscopic phases of spacetime geometry, and we present preliminary evidence for the consistency of these phases with solutions to the equations of motion of classical Hořava-Lifshitz gravity. Apparently, the phase diagram contains a phase transition between a time-dependent de Sitter-like phase and a time-independent phase. We speculate that this phase transition may be understood in terms of deconfinement of the global gravitational Hamiltonian integrated over a spatial 2-sphere.

Non-relativistic holography from Hořava gravity

“…This appears to lead to a unitary, power counting renormalizable theory [49,5,3], as evidenced by the fact that now [G H ] = 0. The low energy action 3.5 with an effective z IR = 1 would then be the flow from this UV fixed point due to relevant deformations.…”

“…This determines the entropy to be proportional to the horizon area, while further thermodynamical considerations [43] fix the proportionality constant, 5) where A is the area of the event horizon, k B is the Boltzmann constant, c is the speed of light, is Planck's constant, and G N is Newton's gravitational constant.…”

On a renormalization group scheme for causal dynamical triangulations

“…Following the prescription (2.6), I estimate the 1-point function by the ensemble average N SL 3 (τ ) . For a spacetime manifold of the form S 3 × S 1 , one performs this ensemble average coherently as explained, for instance, in [16]. In figure 3.1(a) I display N SL 3 (τ ) for a representative causal triangulation from a typical ensemble within phase C. In figure 3.1(b) I display N SL 3 (τ ) for this same ensemble.…”

“…These three observables were studied first in [10,4,15] (respectively) and subsequently in [5,7,13,14,16,17,26,31]. I successively discuss the phenomenology of these three observables in subsubsections 3.2.1, 3.2.2, and 3.2.3, paying particular attention to the length scales that each sets.…”

Matrix Models Techniques and 2d Causal Quantum Gravity

“…For a detailed analysis of the differences between DT and CDT see [38,43,44,45,46]. In recent years physicists have found evidence of a possible connection between CDT and Hoȓava-Lifshitz gravity, first in [47] and later by [48,49], where the value of the spectral dimension is the same for both theories in four dimensions as well as other similarities (such as the phase diagram), opening a new outstanding overlap of approaches to quantum gravity (similarly to the overlap between twistor theory and string theory). In this Thesis we focus on the two-dimensional problem.…”