Ambitwistor Yang-Mills Theory Revisited

• Main Authors: Borsten, Leron, Jurco, Branislav, Kim, Hyungrok, Saemann, Christian, Wolf, Martin
• Format: Journal Article
• Language: English
• Published: 29.08.2024
• Subjects: Mathematics - Mathematical Physics; Physics - High Energy Physics - Theory; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.2408.16727

Inspired by the Movshev-Mason-Skinner Cauchy-Riemann (CR) ambitwistor approach, we provide a rigorous yet elementary construction of a twisted CR holomorphic Chern-Simons action on CR ambitwistor space for maximally supersymmetric Yang-Mills theory on four-dimensional Euclidean space. The key ingredient in our discussion is the homotopy algebraic perspective on perturbative quantum field theory. Using this technology, we show that both theories are semi-classically equivalent, that is, we construct a quasi-isomorphism between the cyclic $L_\infty$-algebras governing both field theories. This confirms a conjecture from the literature. Furthermore, we also show that the Yang-Mills action is obtained by integrating out an infinite tower of auxiliary fields in the Chern-Simons action, that is, the two theories are related by homotopy transfer. Given its simplicity, this Chern-Simons action should form a fruitful starting point for analysing perturbative properties of Yang-Mills theory.