Soft Theorem of N=4 SYM in Grassmannian Formulation

TL;DR

The paper demonstrates that the soft theorem for tree-level amplitudes in $\mathcal{N}=4$ SYM can be derived directly from the Grassmannian contour integral representation. By employing an inverse-soft operation and a carefully chosen gauge, the authors show a universal leading soft factor $S^{(0)} = \frac{\langle n-1,1\rangle}{\langle n-1,n\rangle \langle n1\rangle}$ and a subleading operator $S^{(1)}$ that acts on the anti-holomorphic spinors and supercharges, valid for all $N^{k-2}$MHV levels. The analysis highlights that a single specific sequence of zero-minor constraints drives the soft divergence, while non-consecutive minors decouple in the limit, enabling a compact, perturbative-soft expansion across all helicity sectors. This work thus unifies soft-limit behavior with Grassmannian methods in a supersymmetric setting, providing a practical route to higher-point amplitudes via inverse-soft recursions.

Abstract

Inspired by the new soft theorem in gravity by Cachazo and Strominger, the soft theorem for color-ordered Yang-Mills amplitudes has also been identified by Casali. In this note, the same content of N=4 SYM using the Grassmannian formulation is studied. Explicitly, in the holomorphic soft limit, we reduce the n-particle amplitude in terms of Grassmannian contour integrations into the deformed (n-1)-particle amplitude by localizing k variables relevant to the n-th particle. Afterwards, the leading soft factor and sub-leading soft operator naturally emerge.