Gauge independent kinematic algebra of self-dual Yang-Mills theory

Abstract

The double copy programme relies crucially on the so-called color-kinematics duality which, in turn, is widely believed to descend from a kinematic algebra possessed by gauge theories. In this paper we construct the kinematic algebra of gauge invariant and off-shell self-dual Yang-Mills theory, up to trilinear maps. This structure is a homotopy algebra of the same type as the ones recently uncovered in Chern-Simons and full Yang-Mills theories. To make contact with known results for the self-dual sector, we show that it reduces to the algebra found by Monteiro and O'Connell upon taking light-cone gauge and partially solving the self-duality constraints. Finally, we test a double copy prescription recently proposed in [1] and reproduce self-dual gravity.

26 pages. Published version

References in corpus (33)

• New Relations for Gauge-Theory Amplitudes
• Double Field Theory
• Minimal Basis for Gauge Theory Amplitudes
• The Kinematic Algebra From the Self-Dual Sector
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Double Copy from Homotopy Algebras
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• The convolutional double copy: a case study with a point
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• A double copy for asymptotic symmetries in the self-dual sector
• Two-Loop Renormalization of Quantum Gravity Simplified
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Celestial chiral algebras, colour-kinematics duality and integrability
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Double Field Theory as the Double Copy of Yang-Mills
• New heavenly double copies
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• Non-perturbative aspects of the self-dual double copy
• Gauge $\times$ Gauge on Spheres
• Kinematic Hopf algebra for amplitudes and form factors
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• BRST Symmetry and the Convolutional Double Copy
• One-loop same helicity four-point amplitude from shifts

Cited by in corpus (5)

• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Ambitwistor Yang-Mills Theory Revisited