Refined topological vertex for a 5D $Sp(N)$ gauge theory with antisymmetric matter

TL;DR

This paper applies the refined topological vertex method to compute Nekrasov partition functions for 5D Sp(N) gauge theories with antisymmetric matter, confirming results with the ADHM approach and exploring Higgsing effects.

Contribution

It introduces a refined topological vertex computation for 5D Sp(N) theories with antisymmetric matter, extending previous methods and analyzing Higgsing effects on Kähler parameters.

Findings

Agreement with ADHM results for Nekrasov partition functions

Identification of Kähler parameter tuning related to Higgsing

Application of refined topological vertex to complex gauge theories

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 ADHM method. We also discuss a particular tuning of K\"ahler parameters associated with this Higgsing.