Supersymmetric Wilson loops on S^3

TL;DR

This paper analyzes supersymmetric Wilson loops in N=4 super Yang-Mills theory on S^3, exploring their supersymmetry properties, dual string solutions, and potential connections to two-dimensional bosonic Yang-Mills theory.

Contribution

It introduces a detailed study of supersymmetric Wilson loops on S^3, including explicit string duals and a novel almost complex structure on AdS_4 x S^2.

Findings

String solutions satisfy a first order differential equation.

Loops on S^2 may be computed via 2D bosonic YM.

Certain loops preserve up to 16 supercharges.

Abstract

This paper studies in great detail a family of supersymmetric Wilson loop operators in N=4 supersymmetric Yang-Mills theory we have recently found. For a generic curve on an S^3 in space-time the loops preserve two supercharges but we will also study special cases which preserve 4, 8 and 16 supercharges. For certain loops we find the string theory dual explicitly and for the general case we show that string solutions satisfy a first order differential equation. This equation expresses the fact that the strings are pseudo-holomorphic with respect to a novel almost complex structure we construct on AdS_4 x S^2. We then discuss loops restricted to S^2 and provide evidence that they can be calculated in terms of similar observables in purely bosonic YM in two dimensions on the sphere.