Refined topological vertex for a 5D S p ( N ) gauge theories with antisymmetric matter

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.