Couplings of gravity to antisymmetric gauge fields

TL;DR

This paper classifies all consistent first-order couplings of gravity with 2-form gauge fields using BRST cohomology, confirming previous results that certain geometrical theories are inconsistent or trivial.

Contribution

It provides a comprehensive classification of first-order vertices for gravity coupled to 2-form gauge fields without restrictions on derivatives or gravity action form.

Findings

Consistent deformations are at most linear in the 2-form.

Geometrical theories from nonsymmetric gravity are inconsistent or trivial.

No assumptions on derivative degree or gravity action shape.

Abstract

We classify all the first-order vertices of gravity consistently coupled to a system of 2-form gauge fields by computing the local BRST cohomology H(s|d) in ghost number 0 and form degree n. The consistent deformations are at most linear in the undifferentiated two-form, confirming the previous results of [1] that geometrical theories constructed from a nonsymmetric gravity theory are physically inconsistent or trivial. No assumption is made here on the degree of homogeneity in the derivatives nor on the form of the gravity action.