Horava Gravity with Mixed Derivative Terms: Power-Counting Renormalizability with Lower-Order Dispersions

TL;DR

This paper investigates Horava gravity extended with mixed derivative terms, demonstrating the existence of power-counting renormalizable and unitary models, thus proposing a new class of consistent theories with modified dispersion relations.

Contribution

It shows that Horava gravity with mixed derivatives can be power-counting renormalizable and unitary, countering previous concerns about lower-order dispersions.

Findings

Models with mixed derivatives are renormalizable and unitary.

Mixed derivative terms lead to lower-order dispersion relations.

A new class of consistent Horava gravity-like theories is identified.

Abstract

It has been argued that Horava gravity needs to be extended to include terms that mix spatial and time derivatives in order avoid unacceptable violations of Lorentz invariance in the matter sector. In an earlier paper we have shown that including such mixed derivative terms generically leads to 4th instead of 6th order dispersion relations and this could be (naively) interpreted as a threat to renormalizability. We have also argued that power-counting renormalizability is not actually compromised, but instead the simplest power-counting renormalizable model is not unitary. In this paper we consider the Lifshitz scalar as a toy theory and we generalize our analysis to include higher order operators. We show that models which are power-counting renormalizable and unitary do exist. Our results suggest the existence of a new class of theories that can be thought of as Horava gravity with mixed derivative terms.