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 [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. 
Xavier Bekaert, Bernard Knaepen and Christiane Schomblond