Associativity of One-Loop Corrections to the Celestial Operator Product Expansion

Abstract

There has been recent interest in the question of whether QCD collinear singularities can be viewed as the operator product expansion of a two-dimensional conformal field theory. 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 singularities 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.