Lectures on curved beta-gamma systems, pure spinors, and anomalies

TL;DR

This paper investigates the curved beta-gamma system on pure spinor space, analyzing anomalies and demonstrating conditions for anomaly cancellation, thereby supporting the consistency of Berkovits superstring quantization.

Contribution

It provides a detailed analysis of anomalies in the curved beta-gamma system on pure spinors and shows how they can be canceled, confirming the consistency of the pure spinor superstring approach.

Findings

Anomalies can be canceled under certain conditions.

The pure spinor sigma model reproduces known constructions.

Supports the consistency of Berkovits covariant superstring quantization.

Abstract

The curved beta-gamma system is the chiral sector of a certain infinite radius limit of the non-linear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from the worldsheet and target space diffeomorphism anomalies. We analyze the curved beta-gamma system on the space of pure spinors, aiming to verify the consistency of Berkovits covariant superstring quantization. We demonstrate that under certain conditions both anomalies can be cancelled for the pure spinor sigma model, in which case one reproduces the old construction of B.Feigin and E.Frenkel.