UNIQUENESS OF THE FREEDMAN-TOWNSEND INTERACTION VERTEX FOR 2-FORM GAUGE-FIELDS

Let B-mu nu(a) (a = 1,..., N) be a system of N free two-form gauge fie lds, with field strengths H-mu nu rho(a) = 3 partial derivative([mu)B( nu rho)(a)] and free action S-0 equal to (-1/12) integral d(n)x g(ab)H (mu nu rho)(alpha)H(b mu nu rho) (n greater than or equal to 4). It is shown that in n > 4 dimensions, the only consistent local interaction s that can be added to the free action are given by functions of the f ield strength components and their derivatives (and the Chem-Simons fo rms in 5 mod 3 dimensions). These interactions do not modify the gauge invariance B-mu nu(a) --> B-mu nu(a) + partial derivative[(mu)Lambda( nu)] of the free theory. By contrast, there exist in n = 4 dimensions consistent interactions that deform the gauge symmetry of the free the ory in a non trivial way. These consistent interactions are uniquely g iven by the well-known Freedman-Townsend vertex. The method of proof u ses the cohomological techniques developed recently in the Yang-Mills context to establish theorems on the structure of renormalized gauge-i nvariant operators.