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

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

2011-01-05

arxiv.org/abs/1101.0872v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

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 $\R^2$. 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.

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