Soft Theorem of N=4 SYM in Grassmannian Formulation

TL;DR

This paper explores the soft theorem in N=4 SYM theory within the Grassmannian formulation, demonstrating how soft limits lead to explicit soft factors and operators through contour integrations.

Contribution

It provides a novel Grassmannian-based derivation of soft theorems in N=4 SYM, connecting soft limits to geometric contour integrations.

Findings

Soft factors and operators emerge naturally from Grassmannian contour integrations.

The holomorphic soft limit reduces n-particle amplitudes to (n-1)-particle amplitudes.

Explicit connection between soft theorems and Grassmannian geometry is established.

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.