Title: Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory Show Chinese title

Title: 三维Chern-Simons理论和ABJM理论中的类光多边形威尔逊圈

Abstract: We study light-like polygonal Wilson loops in three-dimensional Chern-Simons and ABJM theory to two-loop order. For both theories we demonstrate that the one-loop contribution to these correlators cancels. For pure Chern-Simons, we find that specific UV divergences arise from diagrams involving two cusps, implying the loss of finiteness and topological invariance at two-loop order. Studying those UV divergences we derive anomalous conformal Ward identities for n-cusped Wilson loops which restrict the finite part of the latter to conformally invariant functions. We also compute the four-cusp Wilson loop in ABJM theory to two-loop order and find that the result is remarkably similar to that of the corresponding Wilson loop in N=4 SYM. Finally, we speculate about the existence of a Wilson loop/scattering amplitude relation in ABJM theory. Show Chinese abstract

Abstract: 我们研究了三维Chern-Simons理论和ABJM理论中的光型多边形Wilson环，计算到两圈阶。对于这两种理论，我们都证明了这些相关函数的一圈贡献相互抵消。对于纯Chern-Simons理论，我们发现特定的紫外发散来自于涉及两个尖点的图，这表明在两圈阶丢失了有限性和拓扑不变性。通过研究这些紫外发散，我们推导出了n个尖点Wilson环的反常共形Ward恒等式，这些恒等式限制了后者的有限部分为共形不变函数。我们还计算了ABJM理论中的四尖点Wilson环，计算到两圈阶，发现结果与N=4 SYM中相应的Wilson环的结果惊人地相似。最后，我们推测ABJM理论中可能存在Wilson环/散射振幅关系。