标题： 全S矩阵与带有（相对）L-无穷代数的威滕图 显示英文标题

标题： Full S-matrices and Witten diagrams with (relative) L-infinity algebras

摘要： $L_\infty$-代数方法对散射幅度进行了优雅的描述，但未能考虑到$S$-矩阵的平凡部分。我们认为，$S$-矩阵的平凡贡献应由另一个互补的$L_\infty$-代数来考虑，从而使得微扰场论由循环相对$L_\infty$-代数来描述。我们进一步证明，这种构造能够重现AdS/CFT中出现的维滕图，特别是对应于CFT两点函数的平凡维滕图。我们还使用这种方法讨论了在有边界流形上的Chern-Simons理论和Yang-Mills理论。 显示英文摘要

摘要： The $L_\infty$-algebra approach to scattering amplitudes elegantly describes the nontrivial part of the $S$-matrix but fails to take into account the trivial part. We argue that the trivial contribution to the $S$-matrix should be accounted for by another, complementary $L_\infty$-algebra, such that a perturbative field theory is described by a cyclic relative $L_\infty$-algebra. We further demonstrate that this construction reproduces Witten diagrams that arise in AdS/CFT including, in particular, the trivial Witten diagrams corresponding to CFT two-point functions. We also discuss Chern-Simons theory and Yang-Mills theory on manifolds with boundaries using this approach.