Refined topological vertex with ON-planes

TL;DR

This paper introduces a refined topological vertex formalism for 5-brane systems with ON-planes, enabling precise computation of partition functions for complex gauge theories, and confirms its validity through agreement with known results.

Contribution

It develops a new refined topological vertex formalism incorporating ON-planes, expanding computational tools for 5-brane web theories and related gauge theories.

Findings

Successfully computes partition functions for 6d E-string theory on a circle.

Accurately calculates 5d SU(3) theory partition function at Chern-Simons level 9.

Results match known theoretical predictions, validating the new formalism.

Abstract

We propose refined topological vertex formalism for 5-brane systems with ON-planes by introducing a new vertex associated with reflection over an ON-plane, which gives rise to new vertex and edge factors. We test our proposal against various 5d $\mathcal{N}=1$ gauge theories which can be realized as 5-brane webs with ON-planes, which include $D$-type quiver theories. In particular, we compute the refined partition functions for 6d E-string theory on a circle as well as 5d SU(3) theory at the Chern-Simons level 9, which can be realized as 5-brane webs with two ON-planes. Our results completely agree with the known results.