A super MHV vertex expansion for N=4 SYM theory

TL;DR

This paper introduces a supersymmetric extension of the MHV vertex expansion for all tree-level amplitudes in N=4 SYM theory, simplifying calculations by reducing the number of diagrams needed.

Contribution

It presents a super MHV vertex expansion depending on Grassmann parameters, derived from a supersymmetric recursion relation, and analyzes its improved large-z behavior.

Findings

Many diagrams vanish with a suitable choice of Grassmann parameters.

Pure-gluon amplitudes require fewer diagrams than in the ordinary expansion.

The expansion's recursion relation is linked to a supersymmetric all-line shift.

Abstract

We present a supersymmetric generalization of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory. In addition to the choice of a reference spinor, this super MHV vertex expansion also depends on four reference Grassmann parameters. We demonstrate that a significant fraction of diagrams in the expansion vanishes for a judicious choice of these Grassmann parameters, which simplifies the computation of amplitudes. Even pure-gluon amplitudes require fewer diagrams than in the ordinary MHV vertex expansion. We show that the super MHV vertex expansion arises from the recursion relation associated with a holomorphic all-line supershift. This is a supersymmetric generalization of the holomorphic all-line shift recently introduced in arXiv:0811.3624. We study the large-z behavior of generating functions under these all-line supershifts, and find that they generically provide 1/z^k falloff at (Next-to)^k MHV level. In the case of anti-MHV generating functions, we find that a careful choice of shift parameters guarantees a stronger 1/z^(k+4) falloff. These particular all-line supershifts may therefore play an important role in extending the super MHV vertex expansion to N=8 supergravity.