Impure Aspects of Supersymmetric Wilson Loops

TL;DR

This paper investigates a broad class of supersymmetric Wilson loops in N=4 super Yang-Mills theory, analyzing their properties, symmetries, and quantum behavior at weak and strong coupling, hinting at potential exact results.

Contribution

It systematically characterizes the scalar couplings and preserved supercharges of these Wilson loops, extending the understanding beyond the standard circular case.

Findings

Explicit weak-coupling computations via Feynman diagrams.

Strong-coupling analysis using AdS/CFT correspondence.

Indications of the possibility for exact evaluation of expectation values.

Abstract

We study a general class of supersymmetric Wilson loops operator in N = 4 super Yang-Mills theory, obtained as orbits of conformal transformations. These loops are the natural generalization of the familiar circular Wilson-Maldacena operator and their supersymmetric properties are encoded into a Killing spinor that is not pure. We present a systematic analysis of their scalar couplings and of the preserved supercharges, modulo the action of the global symmetry group, both in the compact and in the non-compact case. The quantum behavior of their expectation value is also addressed, in the simplest case of the Lissajous contours: explicit computations at weak-coupling, through Feynman diagrams expansion, and at strong-coupling, by means of AdS/CFT correspondence, suggest the possibility of an exact evaluation.