Horava gravity with mixed derivative terms

TL;DR

This paper explores an extended version of Horava gravity with mixed derivative terms, analyzing how these additions influence the theory's propagators, divergences, and renormalizability through perturbative analysis and a toy model.

Contribution

It provides a detailed perturbative analysis of Horava gravity with mixed derivatives and examines their impact on propagators and renormalizability, extending previous models.

Findings

Mixed derivative terms modify propagators and potentially improve divergence behavior.

Including mixed derivatives affects the power counting and renormalizability of the theory.

Toy model analysis supports the role of mixed derivatives in addressing divergences.

Abstract

Horava gravity has been constructed so as to exhibit anisotropic scaling in the ultraviolet, as this renders the theory power-counting renormalizable. However, when coupled to matter, the theory has been shown to suffer from quadratic divergences. A way to cure these divergences is to add terms with both time and space derivatives. We consider this extended version of the theory in detail. We perform a perturbative analysis that includes all modes, determine the propagators and discuss how including mixed-derivative terms affects them. We also consider the Lifshitz scalar with mixed-derivative terms as a toy model for power counting arguments and discuss the influence of such terms on renormalizability.