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

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