Super-Virasoro Anomaly, Super-Weyl Anomaly and the Super-Liouville Action for 2D Supergravity

TL;DR

This paper explores the relationship between super-Virasoro and super-Weyl anomalies in 2D supergravity, constructing actions that cancel or reproduce these anomalies and analyzing their properties and invariance.

Contribution

It explicitly constructs the super-WZW action canceling the super-Virasoro anomaly and introduces a super-Liouville action to restore super-Weyl invariance, providing a local effective gravitational action.

Findings

Constructed super-WZW action canceling super-Virasoro anomaly.

Developed super-Liouville action restoring super-Weyl invariance.

Analyzed BRST invariance in different gauges.

Abstract

The relation between super-Virasoro anomaly and super-Weyl anomaly in $N=1$ NSR superstring coupled with 2D supergravity is investigated from canonical theoretical view point. The WZW action canceling the super-Virasoro anomaly is explicitly constructed. It is super-Weyl invariant but nonlocal functional of 2D supergravity. The nonlocality can be remedied by the super-Liouvlle action, which in turn recovers the super-Weyl anomaly. The final gravitational effective action turns out to be local but noncovariant super-Liouville action, describing the dynamical behavior of the super-Liouville fields. The BRST invariance of this approach is examined in the superconformal gauge and in the light-cone gauge.