论文标题
大型渔网
Massive Fishnets
论文作者
论文摘要
最近，发现无限的大型Feynman积分家族具有意想不到的桑对称性。在无质量的情况下，通过解释单个Feynman积分为相关的相关因子，在Gürdoğan和Kazakov引入的无质量渔网理论中，可以理解相似的一致性。在这里，我们寻求对大型Feynman积分的整合性的类似解释。我们对比两种方法，以在四个维度中定义简单的大规模量子场理论。首先，我们讨论了无质量的双尺度渔网理论中自发的对称破坏。然后，我们通过在库仑分支上采用双尺度n = 4 sym理论，提出了一种大规模渔网理论的替代途径。两种方法都导致了无质量渔网理论的大规模扩展，在群众进入繁殖者的方式方面有所不同。在后一种理论中，平面外壳振幅与确切的那些庞大的Feynman积分一对一是一对一的，这些积分被证明是扬吉人下不变的。这表明对库仑分支N = 4 Sym理论的重新调查。最后，我们证明，在自发对称性破裂的情况下，原始的形式对称性会导致柔软的定理，用于在破碎相中散射振幅。
Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via the interpretation of individual Feynman integrals as correlators in the massless fishnet theory introduced by Gürdoğan and Kazakov. Here we seek for an analogous interpretation of the integrability of massive Feynman integrals. We contrast two approaches to define simple massive quantum field theories in four dimensions. First, we discuss spontaneous symmetry breaking in the massless bi-scalar fishnet theory. We then propose an alternative route to a massive fishnet theory by taking a double-scaling limit of N=4 SYM theory on the Coulomb branch. Both approaches lead to a massive extension of the massless fishnet theory, differing in how masses enter into the propagators. In the latter theory, planar off-shell amplitudes are in one-to-one correspondence with precisely those massive Feynman integrals that were shown to be invariant under the Yangian. This suggests a re-investigation of Coulomb branch N=4 SYM theory with regard to integrability. Finally, we demonstrate that in the case of spontaneous symmetry breaking, the original conformal symmetry leads to soft theorems for scattering amplitudes in the broken phase.
