Ambitwistor Yang-Mills Theory Revisited

TL;DR

This paper constructs a rigorous CR ambitwistor space formulation of maximally supersymmetric Yang-Mills theory, demonstrating semi-classical equivalence with the traditional formulation via homotopy algebraic methods.

Contribution

It provides a novel, elementary construction of a twisted CR holomorphic Chern-Simons action for Yang-Mills theory, confirming a key conjecture and linking it to the standard theory through homotopy transfer.

Findings

Established semi-classical equivalence between the two formulations.

Constructed a quasi-isomorphism between the governing $L_$-algebras.

Showed Yang-Mills action arises from integrating out auxiliary fields.

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 $L_\infty$-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.