Asymptotic freedom in Hořava-Lifshitz gravity.

Area of Science:

• Theoretical physics
• Quantum gravity
• Cosmology

Background:

• Hořava-Lifshitz gravity offers a potential framework for quantum gravity.
• Understanding its renormalization group flow is crucial for its consistency.
• Coupling to matter fields, like Lifshitz scalars, introduces complexities.

Purpose of the Study:

• To investigate the renormalization group flow of projectable Hořava-Lifshitz gravity.
• To analyze the impact of coupling to n Lifshitz scalars.
• To determine the theory's perturbative renormalizability and fixed-point behavior.

Main Methods:

• Application of the Wetterich equation for foliated spacetimes.
• Utilizing novel results for anisotropic heat kernels.
• Explicit computation of matter-induced beta functions for gravitational couplings.

Main Results:

• Identification of an UV attractive anisotropic Gaussian fixed point.
• Observation that Newton's constant vanishes at this fixed point.
• The extra scalar mode decouples, ensuring asymptotic freedom in the large-n expansion.

Conclusions:

• Projectable Hořava-Lifshitz gravity coupled to n Lifshitz scalars is perturbatively renormalizable.
• The identified fixed point suggests a viable high-energy behavior for the theory.
• The fundamental fixed point action deviates from the detailed balance condition.