Invariant Regularization of Supersymmetric Chiral Gauge Theory

We present a regularization scheme which respects the supersymmetry and themaximal background gauge covariance in supersymmetric chiral gauge theories.When the anomaly cancellation condition is satisfied, the effective action inthe superfield background field method automatically restores the gaugeinvariance without counterterms. The scheme also provides a background gaugecovariant definition of composite operators that is especially useful inanalyzing anomalies. We present several applications: The minimal consistentgauge anomaly; the super-chiral anomaly and the superconformal anomaly; as thecorresponding anomalous commutators, the Konishi anomaly and an anomaloussupersymmetric transformation law of the supercurrent (the ``centralextension'' of N=1 supersymmetry algebra) and of the R-current.Comment: uses PTPTeX, 16 pages, based on the invited talk in the workshop on ``Gauge Theory and Integrable Models,'' January 1999, Kyot