Ambitwistor Yang–Mills Theory Revisited

Abstract 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 $$L_\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:math> -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.