Orbifold Vortex and Super Liouville Theory

Abstract

We study the nonabelian vortex counting problem on $\mathbb{C}/\mathbb{Z}_p$. At first we calculate vortex partition functions on the orbifold space using localization techniques, then we find how to extract orbifold vortex partitions function from orbifold linear quiver instanton partition functions. Finally, we study the AGT like relation between orbifold SU(2) vortices and $\mathcal{N} = 1$ super Liouville theory in the mixed R/NS sector by fixing the dictionary among parameters in the common hypergeometric functions system.