# Rank-3 antisymmetric matter on 5-brane webs

## TL;DR

This paper constructs and verifies 5-brane web diagrams for 5d $ ext{SU}(6)$ and $ ext{Sp}(3)$ gauge theories with rank-3 antisymmetric matter, enabling computation of their partition functions.

## Contribution

It introduces new 5-brane web configurations for theories with rank-3 antisymmetric matter and validates them through consistency checks and partition function calculations.

## Key findings

- Proposed 5-brane web diagrams for $SU(6)$ and $Sp(3)$ theories with rank-3 antisymmetric matter.
- Validated web diagrams using one-loop prepotential consistency conditions.
- Computed partition functions using the topological vertex method for these theories.

## Abstract

We discuss Type IIB 5-brane configurations for 5d $\mathcal{N}=1$ gauge theories with hypermultiplets in the rank-3 antisymmetric representation and with various other hypermultiplets, which flow to a UV fixed point at the infinite coupling. We propose 5-brane web diagrams for the theories of $SU(6)$ and $Sp(3)$ gauge groups with rank-3 antisymmetric matter and check our proposed 5-brane webs against several consistency conditions implied from the one-loop corrected prepotential. Using the obtained 5-brane webs for rank-3 antisymmetric matter, we apply the topological vertex method to compute the partition function for one of these $SU(6)$ gauge theories.