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High Energy Physics - Theory

arXiv:2111.08879 (hep-th)
[Submitted on 17 Nov 2021]

Title:Quantizing local holomorphic field theories on twistor space

Authors:Kevin J. Costello
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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.
Subjects: High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)
Cite as: arXiv:2111.08879 [hep-th]
  (or arXiv:2111.08879v1 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2111.08879

Submission history

From: Kevin Costello [view email]
[v1] Wed, 17 Nov 2021 03:12:59 UTC (549 KB)
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