Engineering adjoint hypermultiplet

Abstract.

We study the topological string partition function of a class of toric Calabi-Yau threefold with compact dual web diagrams. These compact web diagrams are compactification of the web diagrams engineering pure five-dimensional SU(N) gauge theory with zero Chern-Simons term. We show, by calculating the topological string partition function, that the corresponding gauge theory is the SU(N) gauge theory with an adjoint hypermultiplet on $\mathbb{R}^{4}\times T^2$ . The advantage of this brane web is that the decoupling limit in which the mass of the hypermultiplet goes to infinity can be taken directly without the needs for any flop transitions (in the dual Calabi-Yau threefold). Also it makes manifest the symmetry of the partition function under the exchange of the mass of the adjoint hypermultiplet and one of the other Kähler parameters associated with complex structure of T².