IAS Amplitudes Group Meeting

Abstract: It is well-known that amplitudes in Yang-Mills theory are severely constrained by the requirement of gauge invariance. In this talk, I will explore two aspects of YM amplitudes where (surface) gauge invariance plays a paramount role. First, after carefully defining a four-dimensional soft limit, I will perform the soft expansion of the YM amplitude and surface integrand in scalar-scaffold variables. In addition to known results, we will see the appearance of novel all-soft-order sum rules at tree-level and a universal leading term for the loop integrand, both coming from gauge invariance. Next, I will discuss a simple differential operator that eliminates the polarization of a particular gluon, whose form is suggested by gauge invariance. Applied to all but two gluons, this operator turns YM theory into Tr ϕ³  theory, both at tree- and loop-level, and has connections to “split” factorizations.