Relating Weyl and diffeomorphism anomalies on super Riemann surfaces

TL;DR

This paper explores the relationship between Weyl and superdiffeomorphism anomalies on super Riemann surfaces, introducing a counterterm involving the Verlinde functional to connect these anomalies and aiding in superconformal field theory analysis.

Contribution

It introduces a specific counterterm that links super Weyl and superdiffeomorphism anomalies using the Verlinde functional extension.

Findings

Derived the local counterterm from the Wess-Zumino action

Connected super Weyl anomaly to superdiffeomorphism anomaly

Facilitated analysis of holomorphic factorization in superconformal theories

Abstract

Starting from the Wess-Zumino action associated to the super Weyl anomaly, we determine the local counterterm which allows to pass from this anomaly to the chirally split superdiffeomorphism anomaly (as defined on a compact super Riemann surface without boundary). The counterterm involves the graded extension of the Verlinde functional and the results can be applied to the study of holomorphic factorization of partition functions in superconformal field theory.