BRST symmetry and unitarity of the Horava theory

TL;DR

This paper analyzes the BRST symmetry in the Horava gravity theory using BFV quantization, demonstrating its invariance, nilpotence, and implications for unitarity and renormalization.

Contribution

It provides a detailed analysis of BRST symmetry in Horava theory, establishing invariance, nilpotence, and unitarity within the BFV quantization framework.

Findings

BRST transformations relate to spatial diffeomorphisms.

Quantum action remains invariant under BRST transformations.

Unitarity of the quantum Horava theory is confirmed.

Abstract

We present an analysis on the BRST symmetry transformations of the Horava theory under the BFV quantization, both in the nonprojectable and projectable cases. We obtain that the BRST transformations are intimately related to a particular spatial diffeomorphism along one of the ghost vector fields. We show explicitly the invariance of the quantum action and the nilpotence of the BRST transformations, using this diffeomorphism largely. The BRST symmetry is verified in the whole phase space, inside and outside the constrained surface. When restricted to the constrained surface, the BRST transformations are completely local. The consistency of the BRST symmetry is a fundamental feature of a quantum field theory, specially for renormalization. The BFV quantization is independent of the chosen gauge-fixing condition. This allows us to show the unitarity of the quantum Horava theory, covering the gauge required for renormalization.