Quantizing local holomorphic field theories on twistor space

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 $WZ{W}_4$ 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 $WZ{W}_4$, 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.

References in corpus (6)

• Supersymmetric gauge theory and the Yangian
• Twistor Actions for Self-Dual Supergravities
• SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry
• Twistor action for general relativity
• Vertex Algebras and Costello-Gwilliam Factorization Algebras
• A Twistor Space Action for Yang-Mills Theory