On BRST Lagrangian description of partially massless bosonic fields

TL;DR

This paper develops a comprehensive BRST Lagrangian framework for partially massless bosonic fields in four-dimensional (A)dS space, clarifying the role of constraints, gauge invariance, and the space's curvature.

Contribution

It introduces a novel conversion of second-class constraints into first-class ones, enabling the construction of a Hermitian, nilpotent BRST charge specifically in de Sitter space.

Findings

BRST charge is Hermitian and nilpotent only in dS space.

The gauge-invariant Lagrangian includes specific St"uckelberg fields.

Equations of motion reproduce the mass shell conditions accurately.

Abstract

We present an exhaustive BRST lagrangian description of partially massless bosonic fields in four-dimensional space. The basic fields are formulated in terms of two-component spin-tensors in (A)dS space where the tracelessness conditions are automatically fulfilled. The mass shell of partially massless fields is reformulated in terms of constraints on Fock space vectors including the second-class constraints. A conversion procedure for transforming second-class constraints into first-class ones is developed, allowing one to construct a Hermitian and nilpotent BRST charge in the Fock space under consideration. It is proven that the hermiticity and nilpotency restrict the conditions on the theory parameters, which are fulfilled only in dS space. The hermiticity of the BRST charge is incompatible with AdS space. The gauge invariant Lagrangian is constructed on the basis of the BRST charge, and for spin $s$ and depth $t$ the allowed states in the Lagrangian include only $(s-t-1)$ St\"uckelberg fields. Their exclusion leads to gauge transformations of degree $(s-t)$ for the physical fields. The Lagrangian equations of motion exactly reproduce the mass shell conditions. The Lagrangian in terms of conventional spin-tensor fields is also presented.