一阶杨-米尔斯费曼图中色-运动学对偶的高阶类似物
Higher-order analogues of colour-kinematics duality in first-order Yang-Mills Feynman diagrams
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中文总结 AI 辅助
该研究针对杨-米尔斯理论标准拉氏量无法显现色-运动学对偶的问题，证明一阶杨-米尔斯作用量的超空间表述存在六阶微分算子，使其费曼图展开满足弱形式的色-运动学对偶。
中文摘要 AI 辅助
色-运动学对偶即便在树图层面，也无法从杨-米尔斯理论的标准拉氏量中直接显现，因为常规的费曼图展开并不满足运动学雅可比恒等式。对于能显现色-运动学对偶的拉氏量而言，费曼图展开的运动学雅可比恒等式，源于作用在去色场代数上的二阶微分算子$\boldsymbol{\rm b}$的存在，该算子是BV$^\boldsymbol{\rm \blacksquare}$-代数结构数据的一部分。我们论证，阶数大于2的微分算子的存在，意味着运动学雅可比恒等式存在更弱但非平凡的片段。我们进一步证明，在巴塔林-维尔科夫斯基形式体系下，一阶杨-米尔斯作用量的超空间表述，在任意时空维度下都存在一个六阶微分算子。因此，杨-米尔斯理论一阶表述的树图和圈图散射振幅的费曼图展开，会自动满足一种弱形式的色-运动学对偶。
英文摘要
Colour-kinematics duality is, even at tree level, not manifest from the standard Lagrangian of Yang-Mills theory in that the usual Feynman-diagram expansion does not follow the kinematic Jacobi identities. For a Lagrangian manifesting colour-kinematics duality, the kinematic Jacobi identities of the Feynman-diagram expansion follow from the existence of a second-order differential operator $\mathsf{b}$ acting on the algebra of colour-stripped fields that forms part of the data of a BV$^\square$-algebra. We argue that the existence of differential operators of order greater than two implies weaker but nontrivial fragments of kinematic Jacobi identities. We further show that a superspace formulation of the first-order Yang-Mills action in the Batalin-Vilkovisky formalism admits a differential operator of order six in every spacetime dimension. Therefore, the Feynman-diagram expansion of tree and loop scattering amplitudes of the first-order formulation of Yang-Mills theory automatically enjoy a weak form of colour-kinematics duality.
