A twistor space action for Yang-Mills theory

2021/03/31 by Alexander D. Popov
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Euclidean space #Holomorphic function #Integrable system #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Space (punctuation) #Twistor space #Twistor theory #hep-th

paper · pdf · doi:10.1103/physrevd.104.026015

published as Phys. Rev. D 104, 026015 (2021) · 18 pages; v2: clarifying comments and a reference added, published version

arxiv created 2021/06/29 · openalex publication_date 2021/07/26 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the twistor space P⁶\ensuremath≅ℝ⁴\ifmmode×\else\texttimes\fiℂP¹ of ℝ⁴ with a nonintegrable almost complex structure J such that the canonical bundle of the almost complex manifold (P⁶,J) is trivial. It is shown that J-holomorphic Chern-Simons theory on a real (6|2)-dimensional graded extension P^6|2 of the twistor space P⁶ is equivalent to self-dual Yang-Mills theory on Euclidean space ℝ⁴ with Lorentz invariant action. It is also shown that adding a local term to a Chern-Simons-type action on P^6|2, one can extend it to a twistor action describing full Yang-Mills theory.

Citations

• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Spinors and Space-Time
• Self-dual sector of QCD amplitudes
• Supertwistors and cubic string field theory for open N=2 strings
• Perturbative Gauge Theory As A String Theory In Twistor Space
• A cubic action for self-dual Yang-Mills