Mirror symmetry and the flavor vortex operator in two dimensions

TL;DR

This paper explores the relationship between the flavor vortex operator in 2D supersymmetric theories and mirror symmetry, revealing that the vortex operator corresponds to an exponential of the mirror dual field.

Contribution

It establishes a precise relation between the flavor vortex operator and the mirror dual twisted chiral multiplet in two-dimensional $ cal=(2,2)$ theories.

Findings

The flavor vortex operator $V_ alpha$ is related to the mirror dual field as $V_ alpha=e^{- alpha y}$.

The work connects disorder operators with mirror symmetry in 2D supersymmetric models.

Abstract

The flavor vortex operator $V_\alpha$ is a local disorder operator defined by coupling a two-dimensional $\mathcal{N}=(2,2)$ chiral multiplet to a non-dynamical gauge field with vortex singularity of holonomy $2\pi\alpha$. We show that it is related to the mirror-dual twisted chiral multiplet, with bottom component $y$, as $V_\alpha=e^{-\alpha y}$.