Supersymmetric Open Wilson Lines

TL;DR

This paper investigates supersymmetric open Wilson lines in N=2 and N=4 supersymmetric Yang-Mills theories, identifying conditions for supersymmetry and exploring perturbative and non-perturbative computation methods.

Contribution

It identifies supersymmetric open Wilson lines in specific supersymmetric theories and discusses their perturbative and potential non-perturbative calculations.

Findings

Supersymmetric OWLs exist only in superconformal N=2 theories.

A semi-circular supersymmetric OWL is found in N=4 SYM with a defect hypermultiplet.

Perturbative calculations are performed, and localization methods are discussed for non-perturbative analysis.

Abstract

In this paper we study Open Wilson Lines (OWL's) in the context of two Supersymmetric Yang Mills theories. First we consider four dimensional N=2 Supersymmetric Yang Mills Theory with hypermultiplets transforming in the fundamental representation of the gauge group, and find supersymmetric OWL's only in the superconformal versions of these theories. We then consider four dimensional N=4 SYM coupled to a three dimensional defect hypermultiplet. Here there is a semi-circular supersymmetric OWL, which is related to the ray by a conformal transformation. We perform a perturbative calculation of the operators in both theories, and discuss using localization to compute them non-perturbatively.