Which antisymmetric gauge fields may couple consistently to supergravity?

Abstract

We deduce from the closure of the supersymmetry algebra at the linearized level on the bosons necessary conditions for the consistency of the coupling of a gauge antisymmetric tensor field A μ1…, μn−1 to supergravity in a d-dimensional space-time. These conditions are: 1. (i) n ⩽ 4 (valid for any d). 2. (ii) d ⩽ 8 (valid for any n). 3. (iii) Chiral d = 10 supergravity (valid for any n). 4. (iv) Chiral d = 14 supergravity ( n ⩽ 4 or n = 7 (selfdual)).