Cohomological BRST aspects of the massless tensor field with the mixed symmetry (k,k)

TL;DR

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

Contribution

It provides a detailed analysis of the local BRST cohomology for tensor fields with mixed symmetry, identifying the possible structures of non-trivial co-cycles and their cohomological components.

Findings

Non-trivial co-cycles stop at antighost number k or k+1.

Last components of co-cycles belong to H(gamma) and H^{inv}(delta|d).

Results clarify the cohomological structure of mixed symmetry tensor fields.

Abstract

The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL(D,R), corresponding to a rectangular, two-column Young diagram with k>2 rows are studied in detail. In particular, it is shown that any non-trivial co-cycle from the local BRST cohomology group H(s|d) can be taken to stop either at antighost number (k+1) or k, its last component belonging to the cohomology of the exterior longitudinal derivative H(gamma) and containing non-trivial elements from the (invariant) characteristic cohomology H^{inv}(delta|d).