Quantizing local holomorphic field theories on twistor space

TL;DR

This paper explores the quantization of local holomorphic field theories on twistor space, revealing their rational correlation functions and the necessity of anomaly cancellation mechanisms involving additional fields.

Contribution

It introduces a framework for quantizing holomorphic theories on twistor space and analyzes anomaly cancellation via Green-Schwarz mechanisms in specific models.

Findings

Correlation functions are rational functions.

Anomaly cancellation requires additional fields.

Specific groups allow consistent anomaly cancellation.

Abstract

This paper studies a class of four-dimensional quantum field theories which arise by quantizing local holomorphic field theories on twistor space. These theories have some remarkable properties: in particular, all correlation functions are rational functions. The two main examples are the $WZW_4$ model of Donaldson and Losev, Moore, Nekrasov and Shatashvili, and self-dual Yang-Mills theory. In each case, anomalies on twistor space must be cancelled by a Green-Schwarz mechanism, which introduces additional fields. For $WZW_4$, this only works for $G = SO(8)$ and the additional field is gravitational. For self-dual Yang-Mills, this works for $SU(2)$, $SU(3)$, $SO(8)$ and the exceptional groups, and the additional field is an axion.