Celestial chiral algebras, colour-kinematics duality and integrability

Abstract

We study celestial chiral algebras appearing in celestial holography, using the light-cone gauge formulation of self-dual Yang-Mills theory and self-dual gravity, and explore also a deformation of the latter. The recently discussed $w_{1+\infty }$ algebra in self-dual gravity arises from the soft expansion of an area-preserving diffeomorphism algebra, which plays the role of the kinematic algebra in the colour-kinematics duality and the double copy relation between the self-dual theories. A $W$ deformation of $w_{1+\infty }$ arises from a Moyal deformation of self-dual gravity. This theory is interpreted as a constrained chiral higher-spin gravity, where the field is a tower of higher-spin components fully constrained by the graviton component. In all these theories, the chiral structure of the operator-product expansion exhibits the colour-kinematics duality: the implicit `left algebra' is the self-dual kinematic algebra, while the `right algebra' provides the structure constants of the operator-product expansion, ensuring its associativity at tree level. In a scattering amplitudes version of the Ward conjecture, the left algebra ensures the classical integrability of this type of theories. In particular, it enforces the vanishing of the tree-level amplitudes via the double copy.

23 pages, 1 figure. v2: minor changes, published version. v3: corrected comment on W algebras

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Cited by in corpus (15)

• Kinematic Lie Algebras From Twistor Spaces
• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• All-order celestial OPE in the MHV sector
• Celestial Locality and the Jacobi Identity
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Chiral Higher Spin Gravity and Convex Geometry
• All-order celestial OPE from on-shell recursion
• Detector Operators for Celestial Symmetries
• Constraining higher-spin S-matrices
• Structure of deformed $w_{1+\infty }$ symmetry and topological generalization in Celestial CFT
• $T\bar{T}$ deformed scattering happens within matrices
• Loop corrections versus marginal deformation in celestial holography
• Celestial Quantum Error Correction II: From Qudits to Celestial CFT