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arXiv · 2510.15662

Topological Vertex for Symmetric matter

Sung-Soo Kim·Xiaobin Li·Futoshi Yagi·Rui-Dong Zhu
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Abstract

We propose a novel topological vertex formalism for 5d $\mathcal{N}=1$ SU($N$) gauge theory with a hypermultiplet in the symmetric tensor representation, whose Type IIB brane construction involves an NS5-brane attached to an O7$^+$-plane. Inspired by the identification $\mathrm{O7}^+\sim \mathbb{Z}_2 + 4 \mathrm{D7}$, we introduce two new types of vertices: the $\mathbb{Z}_2$-vertex, which implements the $\mathbb{Z}_2$ orbifold action, and the FD-vertex, which encodes the monodromy cut induced by the O7$^+$-plane. This formalism generalizes the framework presented in arXiv:2412.19655 and establishes a systematic method for computing partition functions for 5-brane configurations that incorporate an O7$^+$-plane. The resulting partition functions are expressed as sums over Young diagrams, providing a powerful computational tool for studying such gauge theories.

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Sung-Soo Kim, Xiaobin Li, Futoshi Yagi, Rui-Dong Zhu. 2025-10-17. Topological Vertex for Symmetric matter. https://arxiv.org/abs/2510.15662

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