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Ambitwistor Yang-Mills Theory Revisited

Leron Borsten, Branislav Jurco, Hyungrok Kim, Christian Saemann, Martin Wolf

TL;DR

This work recasts maximally supersymmetric Yang–Mills theory in four dimensions as a holomorphic Chern–Simons-type theory on CR ambitwistor space, using a twisted CR structure and BV formalism. The authors leverage a homotopy-algebraic dictionary, showing that the twisted CR ambitwistor action is semi-classically equivalent to $ ext{N}=3$ SYM via a cyclic $L_infty$-quasi-isomorphism, and that this equivalence arises from homotopy transfer corresponding to integrating out an infinite tower of auxiliary fields. The construction resolves previous obstructions to a Lagrangian formulation in the supersymmetric setting and supports a geometric route to perturbative properties and colour–kinematics duality in YM theory. The results provide a robust, covariant framework for analyzing perturbative and BV-structured aspects of YM through ambitwistor methods, with potential extensions to loop-level analyses and twistor-based dualities.

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.

Ambitwistor Yang-Mills Theory Revisited

TL;DR

This work recasts maximally supersymmetric Yang–Mills theory in four dimensions as a holomorphic Chern–Simons-type theory on CR ambitwistor space, using a twisted CR structure and BV formalism. The authors leverage a homotopy-algebraic dictionary, showing that the twisted CR ambitwistor action is semi-classically equivalent to SYM via a cyclic -quasi-isomorphism, and that this equivalence arises from homotopy transfer corresponding to integrating out an infinite tower of auxiliary fields. The construction resolves previous obstructions to a Lagrangian formulation in the supersymmetric setting and supports a geometric route to perturbative properties and colour–kinematics duality in YM theory. The results provide a robust, covariant framework for analyzing perturbative and BV-structured aspects of YM through ambitwistor methods, with potential extensions to loop-level analyses and twistor-based dualities.

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 -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.
Paper Structure (31 sections, 13 theorems, 143 equations)

This paper contains 31 sections, 13 theorems, 143 equations.

Table of Contents

  1. Introduction and summary
  2. CR ambitwistor space and supersymmetric Yang--Mills equations
  3. Bosonic CR ambitwistor space
  4. CR ambitwistor space.
  5. CR structure.
  6. Supersymmetric extension and constraint system
  7. Euclidean $\caN=3$ supersymmetry.
  8. Constraint system of $\caN=3$ supersymmetric Yang--Mills theory.
  9. Quasi-isomorphic differential graded Lie algebras
  10. Twisted CR structure.
  11. Quasi-isomorphic CR complex.
  12. Quasi-isomorphic differential graded Lie algebras.
  13. Witten gauge.
  14. CR ambitwistor action and its space-time interpretation
  15. CR ambitwistor action
  16. ...and 16 more sections

Key Result

proposition 1

Under the assumption of $\IR^4$-triviality, the cohomology groups $H^0(\frL_{\rm CR})$ and $H^1(\frL_{\rm CR})$ are isomorphic to the trivial (i.e. constant) linearised gauge transformations and the quotient space of solutions to the linearised $\caN=3$ supersymmetric Yang--Mills equations modulo li

Theorems & Definitions (29)

  • proposition 1
  • proposition 2
  • proof
  • proposition 3
  • proof
  • corollary 1
  • proof
  • proposition 4
  • proof
  • remark 1
  • ...and 19 more