Abstract
We consider type IIB 5-brane web diagrams for a 5D $Sp(N)$ gauge theory with an antisymmetric hypermultiplet and ${N}_{f}$ fundamental hypermultiplets. The corresponding 5-branes can be obtained by Higgsing a 5-brane web for quiver gauge theory. We use the refined topological vertex formalism to compute Nekrasov partition functions of 5D $Sp(2)$ theories with one antisymmetric hypermultiplet and flavors. Our results agree with the known results obtained from the Atiyah-Drinfeld-Hitchin-Manin method. We also discuss a particular tuning of K\"ahler parameters associated with this Higgsing.
Highlights
A large class of five-dimensional (5D) N 1⁄4 1 supersymmetric gauge theories [1] can be constructed in type IIB 5-brane webs [2,3] or in M theory on Calabi-Yau threefolds [4,5,6,7]
III, we review the refined topological vertex formalism and discuss a special tuning of Kähler parameters for a 5-brane diagram for a T2 theory, which is associated with the Higgsing of 5-brane webs giving rise to SpðNÞ gauge theories with an antisymmetric hypermultiplet
We computed the Nekrasov partition function for 5D N 1⁄4 1 Spð2Þ gauge theories with an antisymmetric hypermultiplet and Nf ≤ 4 flavors using the refined topological vertex method based on a 5-brane web diagram with the nonzero mass of the antisymmetric matter
Summary
A large class of five-dimensional (5D) N 1⁄4 1 supersymmetric gauge theories [1] can be constructed in type IIB 5-brane webs [2,3] or in M theory on Calabi-Yau threefolds [4,5,6,7]. One can compute the (unrefined) partition function of SpðNÞ theory with Nf ≤ 2N þ 6 flavors based on a 5-brane web using the topological vertex method [40]. 5D SpðNÞ0 theory with an antisymmetric hypermultiplet can be obtained from a Higgsing of an SUð2Þ× SUð4Þ×ÁÁÁ×SUð2NÞ×ÁÁÁ×SUð4Þ×SUð2Þ quiver theory
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