Couplings of gravity to antisymmetric gauge fields

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 Damour et al. [Phys. Rev. D 45 (1992) 3289; D 47 (1993) 1541] 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.