Supersymmetric Wilson loops in N=4 SYM and pure spinors

TL;DR

This paper classifies supersymmetric Wilson loops in N=4 super Yang-Mills theory based on their geometric and algebraic properties, identifying specific contours and supercharges that preserve supersymmetry.

Contribution

It introduces a classification of supersymmetric Wilson loops into two cases and systematically analyzes the associated supercharges and operators in case II.

Findings

Wilson loops are either conformal or pure spinor subspace contours.

All pairs of supercharges and operators in case II are classified.

The geometric and algebraic structure of supersymmetric Wilson loops is clarified.

Abstract

We study supersymmetric Wilson loop operators in four-dimensional N=4 super Yang-Mills theory. We show that the contour of a supersymmetric Wilson loop is either an orbit of some conformal transformation of the space-time (case I), or an arbitrary contour in the subspace where local superalgebra generator is a pure spinor (case II). In the more interesting case II we find and classify all pairs (Q,W) of the supercharges and the corresponding operators modulo the action of the global symmetry group.