Infinite hidden symmetries and integrability of N=4 super-Yang-Mills theory

• Applicant: Professor Dr. Olaf Lechtenfeld
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2020 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 446925065

• Final Report Year: 2023

Final Report Abstract

We are witnessing an increasing role of algebro-geometric methods in the worldwide study of strings, gauge theories and integrable models. Me and my collaborators are participating in this endeavors through the investigation of N=2 strings and their hidden Kac-Moody type symmetries, of topological strings on supertwistor spaces, the corresponding string field theories, holomorphic Chern- Simons and super-Yang-Mills theories, as well as integrable models in lower dimensions. Our studies have given us far-reaching experience with twistor methods, differential geometry, extended supersymmetry and integrability. This competence has been further employed to an improved handling of the infinite hidden symmetries of N=4 supersymmetric Yang-Mills theory. The present project elaborates the twistor description of N=4 super-Yang-Mills theory and its self-dual subsector from the viewpoint of Poisson geometry, Poisson-Lie groups and dressing transformations. The consideration of N=4 super-Yang-Mills theory by twistor methods combined with the methods of Poisson geometry and Poisson-Lie groups has not been addressed before. We fill this gap and study hidden Poisson-Lie symmetries of N=4 supersymmetric Yang-Mills theory.

Publications

• A twistor space action for Yang-Mills theory. Physical Review D, 104(2).
  Popov, Alexander D.
  
• On exact solvability of N = 4 super Yang-Mills. Nuclear Physics B, 978, 115742.
  Popov, Alexander D.