Functional Integral Approach to Chiral Anomalies in Supersymmetric Gauge Theories

We formulate anomalous chiral and related Ward-Takahashi identities in supersymmetric-gauge theories, by generalizing Fujikawa’s functional-integral method to superspace. Our approach provides a manifestly supersymmetric and gauge-covariant treatment of the superspace Abelian anomalies, and is applicable to chiral- as well as to left-right symmetric theories. Non-Abelian anomalies are also discussed briefly. Superspace Abelian anomalies imply that particular composite operators,i.e. those containing the associatedU1 currents as a component, exhibit an anomalous supermultiplet structure. We discuss how this leads to various exact relations between scalar and gauge fermion condensates, thereby imposing strong constraints on possible chiral-symmetry realizations in supersymmetric-confining theories.