Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory

Abstract

In this article, we study the localizaiton of the partition function of BPS vortices in $\mathcal{N}=(2,2)$ $U(N)$ super Yang-Mills theory with $N$-flavor on ${\mathbb{R}}^2$. The vortex partition function for $\mathcal{N}=(2,2)$ super Yang-Mills theory is obtained from the one in $\mathcal{N}=(4,4)$ super Yang-Mills theory by mass deformation. We show that the partition function can be written as $Q$-exact form and integration in the partition functions is localized to the fixed points which are related to $N$-tuple one dimensional partitions of positive integers.

15 pages

References in corpus (3)

• The Refined Topological Vertex
• Instantons and Emergent AdS_3 x S^3 Geometry
• Two Proofs of a Conjecture of Hori and Vafa