Renormalization group flow of Hořava-Lifshitz gravity at low energies

Abstract

The functional renormalization group equation for projectable Hořava-Lifshitz gravity is used to derive the non-perturbative beta functions for the Newton's constant, cosmological constant and anisotropy parameter. The resulting coupled differential equations are studied in detail and exemplary RG trajectories are constructed numerically. The beta functions possess a non-Gaussian fixed point and a one-parameter family of Gaussian fixed points. One of the Gaussian fixed points corresponds to the Einstein-Hilbert action with vanishing cosmological constant and constitutes a saddle point with one IR-attractive direction. For RG trajectories dragged into this fixed point at low energies diffeomorphism invariance is restored. The emergence of general relativity from Hořava-Lifshitz gravity can thus be understood as a crossover-phenomenon where the IR behavior of the theory is controlled by this Gaussian fixed point. In particular RG trajectories with a tiny positive cosmological constant also come with an anisotropy parameter which is compatible with experimental constraints, providing a mechanism for the approximate restoration of diffeomorphism invariance in the IR. The non-Gaussian fixed point is UV-attractive in all three coupling constants. Most likely, this fixed point is the imprint of Asymptotic Safety at the level of Hořava-Lifshitz gravity.

Role of the extra coupling in the kinetic term in Hořava-Lifshitz gravity

“…Since renormalization group computations have been initiated in the context of HLG [20,21], it will be interesting to see what flow is realized for λ and whether it is possible to recover some partially gauge-fixed version of the theory while avoiding the strong-coupling pitfalls that have been shown to occur when λ → 1 [22][23][24].…”

A functional renormalization group equation for foliated spacetimes

“…Moreover, the inclusion of matter fields with anisotropic couplings is straightforward. The simplest extension which includes a scale-dependent coupling in the extrinsic curvature terms is currently under investigation and the results will be reported elsewhere [36].…”

“…Thus the anisotropic case of Hořava-Lifshitz gravity allows to introduce further coupling constants in front of the terms. The study of their RG flow will be subject to a future publication [36]. …”

“…2 First results on the RG flow on T pHL including Diff(M)-breaking interactions will be reported elsewhere [36].…”

Effective matter dispersion relation in quantum covariant Horava-Lifshitz gravity

“…[14] uses Exact Renormalisation Group methods to provide an insight into the existence of asymptotically safe gravity [15]. Also, [16] is based on causal dynamical triangulations to study phase transitions of space time geometry in (2+1)-dimensional HL gravity.…”