Yangian Symmetry for Fishnet Feynman Graphs
Yangian Symmetry for Fishnet Feynman Graphs
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DOI：
10.1103/physrevd.96.121901
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发表时间：
2017-07
影响因子：
5
通讯作者：
D. Chicherin;V. Kazakov;F. Loebbert;D. Muller;De-liang Zhong
中科院分区：
文献类型：
--
作者：
D. Chicherin;V. Kazakov;F. Loebbert;D. Muller;De-liang Zhong
证明了各类渔网Feynman图在共形代数上具有杨氏对称性。我们明确地讨论了三维、四维和六维时空中的标量图，以及四维中的费米子的包含。杨氏对称性导致了这些大体上未解的费曼积分族的新的微分方程。值得注意的是，所考虑的三维和四维渔网图在平面的特定双标度极限中控制着关联函数和散射幅度，确保数学{伽马}扭曲的数学{N}=4$SuperYang-Mills或Aharony-Bergman-Jafferis-Maldacena(ABJM)理论。因此，对渔网图的研究使我们能够更深入地了解平面$\mathm{ads}/\mathm{cft}$对应的可积性。
Various classes of fishnet Feynman graphs are shown to feature a Yangian symmetry over the conformal algebra. We explicitly discuss scalar graphs in three, four and six spacetime dimensions as well as the inclusion of fermions in four dimensions. The Yangian symmetry results in novel differential equations for these families of largely unsolved Feynman integrals. Notably, the considered fishnet graphs in three and four dimensions dominate the correlation functions and scattering amplitudes in specific double-scaling limits of planar, $\ensuremath{\gamma}$-twisted $\mathcal{N}=4$ super Yang--Mills or Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. Consequently, the study of fishnet graphs allows us to get deep insights into the integrability of the planar $\mathrm{AdS}/\mathrm{CFT}$ correspondence.