Cancellation of divergences in the nonprojectable Horava theory

TL;DR

This paper demonstrates that all ultraviolet divergences in the nonprojectable Horava gravity cancel out or can be renormalized, supporting its potential renormalizability.

Contribution

It provides a detailed analysis of divergence cancellation in nonprojectable Horava gravity using Hamiltonian formalism and Batalin-Fradkin-Vilkovisky quantization.

Findings

All irregular loop divergences cancel exactly.

Remaining divergences can be removed by local counterterms.

Supports the renormalization of the nonprojectable Horava theory.

Abstract

We perform an analysis of the ultraviolet divergences of the quantum nonprojectable Horava gravity. We work the quantum field theory directly in the Hamiltonian formalism provided by the Batalin-Fradkin-Vilkovisky quantization. In this way the second-class constraints can be incorporated to the quantization. A known local gauge-fixing condition leads to a local canonical Lagrangian. Although the canonical fields acquire regular propagators, irregular propagators persist for the field associated to the measure of the second-class constraints. Loops can be formed with the irregular propagators producing potentially dangerous subdivergences. We show that all these loops cancel exactly between them due to a perfect matching between the propagators and vertices of the fields and ghosts forming the loops. The rest of divergences behaves similiarly to the projectable theory, they can be removed by local counterterms. This result points to the renormalization of the nonprojectable Horava theory.