Chiral higher-spin symmetry of the celestial twistor sphere

TL;DR

This paper explores the structure and properties of chiral higher-spin symmetry algebras on the celestial twistor sphere, revealing their associative nature in anomaly-free cases and their role in constraining twistorial higher-spin theories.

Contribution

It demonstrates the associativity of chiral algebras in anomaly-free theories and analyzes the behavior of form factors in higher-spin celestial twistor theories.

Findings

Chiral algebras are associative in anomaly-free holomorphic theories.

Anomalous theories require axionic currents for associativity.

Non-vanishing higher-spin form factors are observed in Yang-Mills-like interactions.

Abstract

We study the chiral higher-spin symmetry algebras $\mathfrak{ca}$ of various twistorial higher-spin theories. These symmetries play the roles of asymptotic symmetries on the celestial twistor sphere, which constrain the observables of twistorial theories. To first order in quantum correction, we show that the chiral algebras associated with anomaly-free holomorphic twistorial higher-spin theories are associative themselves. On the other hand, the chiral algebras associated with anomalous holomorphic twistorial higher-spin theories only become associative upon including suitable axionic currents. When computing $4d$ form factors in terms of correlation functions between higher-spin currents on the celestial twistor sphere, we observe that there are some non-vanishing higher-spin form factors. This observation, however, is only well justified for the case of theories with Yang-Mills-like interactions. We also give some brief comments on the case of higher-derivative interactions.