Invariant Regularization of Supersymmetric Chiral Gauge Theory. II

TL;DR

This paper completes the construction of a supersymmetric gauge-covariant regularization for chiral gauge theories, analyzing anomalies and anomalies' implications within a consistent supersymmetric framework.

Contribution

It introduces a manifestly supersymmetric regularization scheme and evaluates gauge anomalies, proving current integrability and calculating superconformal anomalies.

Findings

Covariant gauge anomaly evaluated

Integrability of gauge current proven in anomaly-free cases

One-loop superconformal anomaly calculated

Abstract

By undertaking additional analyses postponed in a previous paper, we complete our construction of a manifestly supersymmetric gauge-covariant regularization of supersymmetric chiral gauge theories. We present the following: An evaluation of the covariant gauge anomaly; a proof of the integrability of the covariant gauge current in anomaly-free cases; a calculation of a one-loop superconformal anomaly in the gauge supermultiplet sector. On the last point, we find that the ghost-anti-ghost supermultiplet and the Nakanishi-Lautrup supermultiplet give rise to BRST exact contributions which, due to ``tree-level'' Slavnov-Taylor identities in our regularization scheme, can safely be neglected, at least at the one-loop level.