Twistor Parametrization of Locally BPS Super-Wilson Loops

Cristian Vergu

doi:10.1155/2017/4852015

Abstract

We consider the kinematics of the locally BPS super-Wilson loop in 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 the product of two super-Grassmannian manifolds G2∣2(4∣4)×G2∣2(4∣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 superdeterminants.

Highlights

Citing this paper Please note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version
The dual superconformal symmetry is one of the more surprising and unexpected results arising from studies of scattering amplitudes in N = 4 theory
The Yangian symmetry is at the core of the duality between polygonal super-Wilson loops and scattering amplitudes; in particular it contains both the conformal group acting on scattering amplitudes and the dual conformal group acting on super-Wilson loops

Summary

Introduction

The dual superconformal symmetry is one of the more surprising and unexpected results arising from studies of scattering amplitudes in N = 4 theory It started as an observation (see [1]) of an inversion symmetry property of integrals appearing the perturbative expansion. Reference [17] asked the question of whether it was possible to avoid the cusps (and the divergences) while still preserving the Yangian symmetry They found that this is possible but, besides the coupling to the gauge field A, they had to add a coupling of the scalars φ as well, in a way which would correspond to the dimensional reduction of a light-like Wilson loop in ten-dimensional N = 1 super-Yang-Mills theory. We hope that this parametrization, besides making the superconformal symmetry manifest, will be useful in finding the Yangian invariants as well, along the lines of [23,24,25]

Kinematics

Pure Spinor Parametrization

Supersymmetrization

Correlation Functions

Findings

Harmonic Superspace