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.

中文翻译：

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单环校正对天体算子乘积展开的结合性

QCD 共线奇点是否可以被视为二维共形场论的算子积展开，这一问题最近引起了人们的兴趣。我们分析了这个问题的一个版本，以了解纯规范理论的自对偶极限（包含两个螺旋的状态）。我们表明已知的单环共线奇点不会形成结合手性代数。结合性的失败可以追溯到扭量空间上的一个新的规范反常。我们发现，如果我们引入一个不寻常的轴子，它可以通过 Green-Schwarz 机制消除扭量空间异常，则可以恢复某些规范群的结合性。或者，可以使用精心选择的物质为某些规范群恢复结合性。