Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter

TL;DR

This paper employs localization to exactly compute supersymmetric Wilson loop expectation values in superconformal Chern-Simons theories with matter, reducing the problem to a non-Gaussian matrix model applicable to various models.

Contribution

It introduces a method to compute Wilson loops in N=2 superconformal Chern-Simons theories with matter using localization, extending previous results to a broader class of theories.

Findings

Exact Wilson loop values for pure Chern-Simons with U(N) match known results.

Agreement with perturbative calculations in ABJM theory.

Method applicable to Gaiotto-Witten, BLG, and related theories.

Abstract

We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N=2 theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.