# Supersymmetric Wilson loops in two dimensions and duality

## TL;DR

This paper classifies and analyzes supersymmetric Wilson loops in two-dimensional theories, demonstrating their invariance under deformations, their computability via localization, and their behavior under dualities.

## Contribution

It provides a comprehensive classification of supersymmetric Wilson loops in 2D and establishes their invariance, exact computability, and duality mappings.

## Key findings

- Wilson loops are invariant under smooth contour deformations.
- They can be mapped to local operators at genus zero.
- The duality map of Wilson loop correlators is explicitly derived.

## Abstract

We classify bosonic $\mathcal{N}=(2,2)$ supersymmetric Wilson loops on arbitrary backgrounds with vector-like R-symmetry. These can be defined on any smooth contour and come in two forms which are universal across all backgrounds. We show that these Wilson loops, thanks to their cohomological properties, are all invariant under smooth deformations of their contour. At genus zero they can always be mapped to local operators and computed exactly with supersymmetric localisation. Finally, we find the precise map, under two-dimensional Seiberg-like dualities, of correlators of supersymmetric Wilson loops.