Counterterms in semiclassical Horava-Lifshitz gravity

Abstract

We analyze the semiclassical Hořava-Lifshitz gravity for quantum scalar fields in 3+1 dimensions. The renormalizability of the theory requires that the action of the scalar field contains terms with six spatial derivatives of the field, i.e. in the UV, the classical action of the scalar field should preserve the anisotropic scaling symmetry ($t\to L^{2z}t,$ $\vec{x}\to L^2\vec{x}$, with $z=3$) of the gravitational action. We discuss the renormalization procedure based on adiabatic subtraction and dimensional regularization in the weak field approximation. We verify that the divergent terms in the adiabatic expansion of the expectation value of the energy-momentum tensor of the scalar field contain up to six spatial derivatives, but do not contain more than two time derivatives. We compute explicitly the counterterms needed for the renormalization of the theory up to second adiabatic order and evaluate the associated $\beta$ functions in the minimal subtraction scheme.

8 pages

References in corpus (10)

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Cited by in corpus (19)

• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• Hořava Gravity at a Lifshitz Point: A Progress Report
• Renormalization of Horava Gravity
• Do we have unitary and (super)renormalizable Quantum Gravity below Planck scale?
• A functional renormalization group equation for foliated spacetimes
• Asymptotic freedom in Horava-Lifshitz gravity
• Status of Horava gravity: A personal perspective
• Renormalization group flow of Hořava-Lifshitz gravity at low energies
• One-loop renormalization in a toy model of Horava-Lifshitz gravity
• Gödel-type universes and chronology protection in Horava-Lifshitz gravity
• Heat kernel methods for Lifshitz theories
• Quantization of Horava Gravity in 2+1 Dimensions
• Quantization of (1+1)-dimensional Hořava-Lifshitz theory of gravity
• Matter in Horava-Lifshitz gravity
• Lifshitz scalar fields: one loop renormalization in curved backgrounds
• One-loop effective potential in nonlocal scalar field models
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• Quantum effective action for degenerate vector field theories
• Black Holes in Ultraviolet-Complete Horava Gravity