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Extended BRST cohomology, consistent deformations and anomalies of four-dimensional supersymmetric gauge theories
The local cohomology of an extended BRST differential which includes global N=1 supersymmetry and Poincaré transformations is completely and explicitly computed in four-dimensional supersymmetric gauge theories with super-Yang-Mills multiplets, chiral matter multiplets and linear multiplets containing 2-form gauge potentials.
In particular we determine to first order all N=1 supersymmetric and Poincar invariant consistent deformations of these theories that preserve the N=1 supersymmetry algebra on-shell modulo gauge transformations, and all Poincaré invariant candidate gauge and supersymmetry anomalies.
When the Yang-Mills gauge group is semisimple and no linear multiplets are present, we find that all such deformations can be constructed from standard superspace integrals and preserve the supersymmetry transformations in a formulation with auxiliary fields, and the candidate anomalies are exhausted by supersymmetric generalizations of the well-known chiral anomalies. In the general case there are additional deformations and candidate anomalies which are relevant especially to the deformation of free theories and the general classification of interaction terms in supersymmetric field theories.