On the associativity of one-loop corrections to the celestial OPE

TL;DR

This paper investigates the algebraic structure of one-loop corrections in celestial OPE within self-dual gauge theories, revealing non-associativity due to a twistor space anomaly and proposing mechanisms to restore associativity.

Contribution

It demonstrates that one-loop collinear singularities do not form an associative algebra and proposes anomaly cancellation methods to restore associativity in celestial OPE.

Findings

One-loop collinear singularities are non-associative.

A gauge anomaly on twistor space causes non-associativity.

Introducing an axion or specific matter content restores associativity.

Abstract

There has been recent interest in the question of whether QCD collinear singularities can be viewed as the OPE of a two-dimensional CFT. We analyze a version of this question for the self-dual limit of pure gauge theory (incorporating states of both helicities). We show that the known one-loop collinear singulaties do not form an associative chiral algebra. The failure of associativity can be traced to a novel gauge anomaly on twistor space. We find that associativity can be restored for certain gauge groups if we introduce an unusual axion, which cancels the twistor space anomaly by a Green-Schwarz mechanism. Alternatively, associativity can be restored for some gauge groups with carefully chosen matter.