Mirror symmetry and the flavor vortex operator in two dimensions

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 $V_{\alpha }=e^{-\alpha y}$.