BRST cohomological results on the massless tensor field with the mixed symmetry of the Riemann tensor

TL;DR

This paper investigates the BRST cohomological properties of a free, massless tensor field with Riemann tensor symmetry, revealing the structure of non-trivial co-cycles and their relation to characteristic cohomology.

Contribution

It provides a detailed analysis of the local BRST cohomology for such tensor fields, showing that non-trivial co-cycles are limited to antighost number three and relate to invariant characteristic cohomology.

Findings

Non-trivial co-cycles stop at antighost number three

Last component of co-cycles belongs to cohomology of exterior longitudinal derivative

Contains non-trivial elements from invariant characteristic cohomology

Abstract

The basic BRST cohomological properties of a free, massless tensor field with the mixed symmetry of the Riemann tensor are studied in detail. It is shown that any non-trivial co-cycle from the local BRST cohomology group can be taken to stop at antighost number three, its last component belonging to the cohomology of the exterior longitudinal derivative and containing non-trivial elements from the (invariant) characteristic cohomology.