Twistor Parametrization of Locally BPS Super-Wilson Loops

TL;DR

This paper introduces a twistorial framework for analyzing the kinematics of locally BPS super-Wilson loops in N=4 super-Yang-Mills, revealing new geometric descriptions and simplifying the scalar correlation functions at one loop.

Contribution

It provides a novel twistorial parametrization of super-Wilson loop kinematics using supersymmetrized pure spinors and Grassmannian spaces, simplifying one-loop scalar correlator calculations.

Findings

Kinematics described by supersymmetrized pure spinors

Kinematics represented as points in a Grassmannian product space

Scalar correlation functions expressed as sums of super-determinants

Abstract

We consider the kinematics of the locally BPS super-Wilson loop in $\mathcal{N}=4$ super-Yang-Mills with scalar coupling from a twistorial point of view. We find that the kinematics can be described either as supersymmetrized pure spinors or as a point in $G_{2\vert 2}(4\vert 4) \times G_{2\vert 2}(4\vert 4)$. In this description of the kinematics the scalar--scalar correlation function appearing in the one-loop evaluation of the super-Wilson loop can be neatly written as a sum of four super-determinants.