One-loop renormalization in a toy model of Horava-Lifshitz gravity

Abstract

We present a one loop calculation in the context of Horava-Lifshitz gravity. Due to the complexity of the calculation in the full theory we focus here on the study of a toy model, namely the conformal reduction of the z=2 projectable theory in 2+1 dimensions. For this value of the dimension there are no gravitons, hence the conformal mode is the only physical degree of freedom, and thus we expect our toy model to lead to qualitatively correct answers regarding the perturbative renormalization of the full theory. We find that Newton's constant (dimensionless in Horava-Lifshitz gravity) is asymptotically free. However, the DeWitt supermetric approaches its Weyl invariant form with the same speed and the effective interaction coupling remains constant along the flow. In other words, the would-be asymptotic freedom associated to the running Newton's constant is exactly balanced by the strong coupling of the scalar mode as the Weyl invariant limit is approached. We conclude that in such model the UV limit is singular at one loop order, and we argue that a similar phenomenon can be expected in the full theory, even in higher dimensions.

18 pages. v2: corrected some misprints, added 3 references, some clarifying comments and a new appendix

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Cited by in corpus (34)

• Hořava Gravity at a Lifshitz Point: A Progress Report
• Renormalization of Horava Gravity
• Hořava gravity is asymptotically free (in 2+1 dimensions)
• Asymptotic freedom in Horava-Lifshitz gravity
• Cosmological bounds on the field content of asymptotically safe gravity-matter models
• Towards the renormalization group flow of Horava gravity in $(3+1)$ dimensions
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• Horava gravity with mixed derivative terms
• Spin-base invariance of Fermions in arbitrary dimensions
• Quantization of Horava Gravity in 2+1 Dimensions
• Cancellation of divergences in the nonprojectable Horava theory
• Quantization of (1+1)-dimensional Hořava-Lifshitz theory of gravity
• More on "Little Lambda" in Hořava-Lifshitz Gravity
• Quantization of the Horava theory at the kinetic-conformal point
• Completing Lorentz violating massive gravity at high energies
• Isotropic Lifshitz critical behavior from the functional renormalization group
• The anisotropic coupling of gravity and electromagnetism in Hořava-Lifshitz theory
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Indications of isotropic Lifshitz points in four dimensions
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• BFV quantization of the nonprojectable 2+1 Horava theory
• Pure electromagnetic-gravitational interaction in Hořava-Lifshitz theory at the kinetic conformal point
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• Quantum Lagrangian of the Horava theory and its nonlocalities
• New Heat Kernel Method in Lifshitz Theories
• Primordial perturbations in a rainbow universe with running Newton constant
• Effective action of the Horava theory: Cancellation of divergences
• Isotropic Lifshitz Scaling in four dimensions
• Renormalization of Supersymmetric Lifshitz Sigma Models
• Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time
• Gravitational waves in Hořava-Lifshitz anisotropic gravity
• Wave zone in the Hořava-Lifshitz theory at the kinetic-conformal point in the low energy regime
• Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory
• Landau Theory of Causal Dynamical Triangulations