Invariant Regularization of Supersymmetric Chiral Gauge Theory

TL;DR

This paper introduces a supersymmetric gauge covariant regularization method for chiral gauge theories that preserves supersymmetry and gauge invariance at the one-loop level, enabling consistent anomaly calculations.

Contribution

The authors develop a manifestly supersymmetric and gauge covariant regularization scheme applicable to chiral gauge theories, ensuring invariance beyond one-loop and clarifying anomaly structures.

Findings

Effective action remains supersymmetric and gauge invariant above one-loop.

Gauge anomaly appears only in one-loop diagrams with background gauge superfield.

Applications include calculations of super-chiral and superconformal anomalies, and anomalous commutators.

Abstract

We formulate a manifestly supersymmetric gauge covariant regularization of supersymmetric chiral gauge theories. In our scheme, the effective action in the superfield background field method above one-loop is always supersymmetric and gauge invariant. The gauge anomaly has a covariant form and can emerge only in one-loop diagrams with all the external lines being the background gauge superfield. We also present several illustrative applications in the one-loop approximation: the self-energy part of the chiral multiplet and of the gauge multiplet; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.