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 $L_{\infty }$-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.

v3: 43 pages, typos fixed and clarifications added, version published in Annales Henri Poincare

References in corpus (48)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Gravity as the Square of Gauge Theory
• Conformal Supergravity in Twistor-String Theory
• $L_{\infty }$ Algebras and Field Theory
• Supersymmetric Gauge Theories in Twistor Space
• Twistor actions for non-self-dual fields; a new foundation for twistor-string theory
• New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Gravity, Twistors and the MHV Formalism
• Noncommutative homotopy algebras associated with open strings
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Double Copy from Homotopy Algebras
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Twistor Actions for Self-Dual Supergravities
• Conformal and Einstein gravity from twistor actions
• Off-Shell Color-Kinematics Duality for Chern-Simons
• An ambitwistor Yang-Mills Lagrangian
• Scattering Amplitude Recursion Relations in BV Quantisable Theories
• The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations
• Kinematic Lie Algebras From Twistor Spaces
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Topological B-Model on Weighted Projective Spaces and Self-Dual Models in Four Dimensions
• On Hidden Symmetries of a Super Gauge Theory and Twistor String Theory
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Loop Amplitudes and Quantum Homotopy Algebras
• On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity
• Quantum $L_{\infty }$ Algebras and the Homological Perturbation Lemma
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
• Self-Dual Supergravity and Twistor Theory
• The Topological B-Model on Fattened Complex Manifolds and Subsectors of N=4 Self-Dual Yang-Mills Theory
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Matrix Models and D-branes in Twistor String Theory
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Homotopy Algebras of Differential (Super)forms in Three and Four Dimensions
• Abstract Hodge decomposition and minimal models for cyclic algebras
• Symmetry Factors of Feynman Diagrams and the Homological Perturbation Lemma
• Colour-kinematics duality, double copy, and homotopy algebras
• Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras
• A Twistor Space Action for Yang-Mills Theory
• On Exact Solvability of $\mathcal{N}$=4 super Yang-Mills