Quantizing local holomorphic field theories on twistor space

Understand

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.