Associativity of celestial OPE, higher spins and self-duality

TL;DR

This paper explores the deep connections between celestial conformal field theory, self-dual theories, and higher-spin interactions, emphasizing the role of OPE associativity and holomorphic constraints in understanding self-duality and gauge algebra structures.

Contribution

It clarifies the relationship between OPE associativity, self-duality, and higher-spin theories, extending the understanding of celestial CFT and cubic vertex constraints.

Findings

OPE associativity constrains celestial CCFT structures

Self-dual theories satisfy OPE associativity and holomorphic constraints

Higher-spin theories with specific interactions are consistent with these constraints

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.