BRST Lagrangian construction for spin-2 field in Einstein space

TL;DR

This paper develops a BRST-based method to construct a gauge-invariant Lagrangian for massive spin-2 fields in Einstein spaces, ensuring hyperbolic and causal propagation and extending partial masslessness concepts.

Contribution

It introduces a novel BRST approach for higher spin fields in Einstein spaces, providing a consistent, gauge-invariant Lagrangian with auxiliary fields for massive spin-2 fields.

Findings

Lagrangian is gauge invariant with auxiliary and Stuckelberg fields.

Propagation of spin-2 field is hyperbolic and causal.

Extended the notion of partial masslessness for spin-2 in Einstein space.

Abstract

We explore a new possibility of BRST construction in higher spin field theory to obtain a consistent Lagrangian for massive spin-2 field in Einstein space. Such approach automatically leads to gauge invariant Lagrangian with suitable auxiliary and Stuckelberg fields. It is proved that in this case a propagation of spin-2 field is hyperbolic and causal. Also we extend notion of partial masslessness for spin-2 field in the background under consideration.