Smooth Wilson Loops in N=4 Non-Chiral Superspace

TL;DR

This paper introduces a smooth supersymmetric Wilson loop operator in 4d N=4 super Yang-Mills theory, extending previous constructions to non-light-like loops in full superspace, and analyzes its properties and vacuum expectation values.

Contribution

It presents a new formulation of supersymmetric Wilson loops in non-chiral superspace, including proofs of finiteness and detailed perturbative calculations.

Findings

Proven finiteness of the Wilson loop's vacuum expectation value at leading order.

Derived explicit vacuum expectation values up to quartic order in anti-commuting coordinates.

Analyzed loops constructed from quadric splines with continuous derivatives at intersections.

Abstract

We consider a supersymmetric Wilson loop operator for 4d N=4 super Yang-Mills theory which is the natural object dual to the AdS_5 x S^5 superstring in the AdS/CFT correspondence. It generalizes the traditional bosonic 1/2 BPS Maldacena-Wilson loop operator and completes recent constructions in the literature to smooth (non-light-like) loops in the full N=4 non-chiral superspace. This Wilson loop operator enjoys global superconformal and local kappa-symmetry of which a detailed discussion is given. Moreover, the finiteness of its vacuum expectation value is proven at leading order in perturbation theory. We determine the leading vacuum expectation value for general paths both at the component field level up to quartic order in anti-commuting coordinates and in the full non-chiral superspace in suitable gauges. Finally, we discuss loops built from quadric splines joined in such a way that the path derivatives are continuous at the intersection.