Anomaly-free twistorial higher-spin theories

TL;DR

This paper develops twistor BV actions for bosonic holomorphic higher-spin theories, demonstrating their classical and quantum consistency, and introduces an index theorem for identifying anomaly-free models.

Contribution

It introduces a framework for anomaly-free twistorial higher-spin theories using BV actions and an index theorem extension.

Findings

Certain subclasses of twistorial higher-spin theories are quantum consistent without anomalies.

An index theorem extension helps identify anomaly-free models.

Mechanisms for anomaly cancellation at one loop are discussed.

Abstract

We present twistor BV actions that encompasses many classically consistent bosonic holomorphic twistorial higher-spin theories with vanishing cosmological constant. Upon quantization, these actions are shown to be quantum consistent, i.e. no gauge anomaly, for some subclasses of twistorial higher-spin theories. Anomaly-free twistorial theories can be identified through an index theorem, which is a higher-spin extension of the Hirzebruch-Riemann-Roch index theorem. We also discuss the anomaly cancellation mechanisms on twistor space to render anomalous theories quantum consistent at one loop.