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)).
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