场论与规范理论非对易形变的新视角
A new perspective on non-commutative deformations of field and gauge theories
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中文总结 AI 辅助
本文基于Drinfel'd扭的星积构造场论与规范理论的非对易形变，扩展了适用扭的范围，证明了费曼图的平面等价性，为研究$\boldsymbol{N}=4$超杨-米尔斯的对偶形变提供了新视角。
中文摘要 AI 辅助
我们基于Drinfel'd扭实施的星积构造了场论与规范理论的非对易形变，可涵盖大量扭，包括由共形对称性和超对称性构建的扭。我们构造的核心思路是采用由未形变理论的对称性构建的扭，这些扭实现为主动对称性变换。我们认为，该构造相当于对已知规范理论形变的重新表述，且显著扩展了适用实例的范围。为确保与规范不变性一致，我们还确定了一个单模性条件，该条件比文献中通常采用的条件更弱，因此可应用原本会被排除的扭。最后，我们还证明了一个平面等价定理，指出形变理论的费曼图保留了未形变的内部结构，扭仅作用于其外腿。所有这些结果对于识别和研究$\boldsymbol{\textit{N}=4}$超杨-米尔斯理论的形变都很重要，该形变被提出作为与$\boldsymbol{AdS_5\times S^5}$超弦的齐次Yang-Baxter形变对偶的理论，但我们的构造和结果的适用性超出了该范围。
英文摘要
We construct non-commutative deformations of field and gauge theories based on star-products implemented by Drinfel'd twists. We are able to encompass a large family of twists, including those built out of conformal symmetries and supersymmetries. The main idea behind our construction is to work with twists constructed from symmetries of the undeformed theory, that are realised as active symmetry transformations. We argue that our construction amounts to a reformulation of known deformations of gauge theories, and that it significantly extends the range of applicable examples. To ensure consistency with gauge invariance, we also identify a unimodularity condition that is weaker than the one that is normally employed in the literature, so that we can apply twists that would otherwise be left out. Finally, we also prove a planar equivalence theorem stating that the Feynman diagrams of the deformed theories retain an undeformed internal structure, with the twist acting only on their external legs. All these results are important to identify and work with deformations of $\mathcal N=4$ super Yang-Mills that are proposed to be dual to homogeneous Yang-Baxter deformations of the $AdS_5\times S^5$ superstring, but the applicability of our construction and results goes beyond that.
