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For any (super) group and hence for any geometrical (super) theory Bianchi identities imply that certain 3-forms vanish. In order to perform a systematic analysis of their implications in the presence of constraints one needs a complete basis of independent 3-forms spanning the 3-form linear space. In this paper we discuss a general procedure for the derivation of such a basis in the case of supersymmetric theories involving commuting spinor l-forms. Our technique is based an the decomposition of the product of group representations into irreducible components and replaces all Fierz rearrangements. We give as example the cases of N = 1, d = 4, N = 2, d = 4 and N = 2, d = 5 supergravity. Then applying our algebraic techniques to the last of these three models, the only other known example, besides N = 1, d = 4 supergravity, of a pure geometrical theory, we derive its off-shell structure containing 48 bosons and 48 fermions. The torsion-like constraints which we itnplement in the Bianchis in order to obtain our set of auxiliary fields are a subset of the complete set of variational equations of the theory so that we derive our off-shell multiplet without any reference to an embedding conformal symmetry. The point with which we still need to use ingenuity is the selection of those equations which are to be kept and those which are to be thrown out.
Trace Anomalies and A(" Theory in Curved Space. S. J.
📜 SIMILAR VOLUMES
The characteristics of various threshold anomalies in cross-sections and phase shifts are investigated and categorized.