New insight into BRST anomalies in superstring theory

TL;DR

This paper provides a comprehensive algebraic analysis of BRST anomalies in superstring theory, identifying the unique super-Virasoro anomaly and deriving the super-Weyl anomaly, along with a novel local super-Liouville action.

Contribution

It introduces a complete algebraic solution to BRST anomaly consistency conditions and constructs a new local super-Liouville action linking different anomalies.

Findings

Identified the unique super-Virasoro anomaly solution.

Derived the super-Weyl anomaly from the super-Virasoro anomaly.

Proposed a novel super-Liouville type action as a Wess-Zumino-Witten term.

Abstract

Based on the extended BRST formalism of Batalin, Fradkin and Vilkovisky, we perform a general algebraic analysis of the BRST anomalies in superstring theory of Neveu-Schwarz-Ramond. Consistency conditions on the BRST anomalies are completely solved. The genuine super-Virasoro anomaly is identified with the essentially unique solution to the consistency condition without any reference to a particular gauge for the 2D supergravity fields. In a configuration space where metric and gravitino fields are properly constructed, general form of the super-Weyl anomaly is obtained from the super-Virasoro anomaly as its descendant. We give a novel local action of super-Liouville type, which plays a role of Wess-Zumino-Witten term shifting the super-Virasoro anomaly into the super-Weyl anomaly. These results reveal a hierarchial relationship in the BRST anoamlies.