Horava Gravity and Gravitons at a Conformal Point

TL;DR

This paper investigates a special point in Horava gravity where an anisotropic Weyl symmetry emerges, leading to the disappearance of scalar gravitons and leaving only tensor modes, suggesting a potential UV fixed point with conformal symmetry.

Contribution

It demonstrates that at $ =1/3$, Horava gravity exhibits UV conformal symmetry and lacks scalar gravitons, highlighting a possible UV fixed point with unique symmetry properties.

Findings

Scalar graviton mode disappears at $ =1/3$

Only tensor graviton modes remain in the spectrum

UV conformal symmetry is linked to detailed balance

Abstract

Recently Horava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorenz invariance in UV. Here, I study the Horava model at $\lambda=1/3$, where an anisotropic Weyl symmetry exists in the UV limit, in addition to the foliation-preserving diffeomorphism. By considering linear perturbations around Minkowski vacuum, I show that the scalar graviton mode is completely disappeared and only the usual tensor graviton modes remain in the physical spectrum. The existence of the UV conformal symmetry is unique to the theory with the detailed balance and it is quite probable that $\lambda=1/3$ be the UV fixed point. This situation is analogous to $\lambda=1$, which is Lorentz invariant in the IR limit and is believed to be the IR fixed point.