Associativity of celestial OPE, higher spins and self-duality

2025/08/22 by Mattia Serrani, Serrani, Mattia
Physics and Astronomy · #hep-th

paper · pdf · doi:10.48550/arxiv.2508.16804

48 pages; v2: minor corrections, references added, journal version

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We highlight and clarify the connection between several ideas and self-dual theories: (a) the operator product expansion (OPE) associativity in celestial conformal field theory (CCFT); (b) the vanishing of tree-level amplitudes; (c) the Jacobi identity for the "gauge" algebra; (d) the light-cone holomorphic constraints. Naturally, (b), (c), or (d) are closely related to self-duality. In particular, the recently classified arXiv:2505.12839 chiral higher-spin theories with one- and two-derivative interactions (i.e. with gauge and gravitational interactions, which are extensions of self-dual Yang-Mills and self-dual gravity) also satisfy the OPE associativity constraint. We discuss the OPE associativity constraint and the holomorphic constraint for the most general class of cubic vertices.

Citations

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Related

• Light-Front approach to 4d massless Higher-Spin interactions
• On the associativity of one-loop corrections to the celestial OPE
• On classification of (self-dual) higher-spin gravities in flat space
• Associativity is enough: an all-orders 2d chiral algebra for 4d form factors
• Celestial OPE in Self Dual Gravity