Topological B-Model, Matrix Models, $\hat{c}=1$ Strings and Quiver Gauge Theories

TL;DR

This paper explores the topological and integrable properties of $=1$ string theories, constructing their ground rings, matrix models, and gauge theory correspondences to deepen understanding of their mathematical structure.

Contribution

It introduces a topological B-model framework for $=1$ strings, linking ground rings to conifold quotients and developing associated matrix models and gauge theories.

Findings

Constructed ground rings as conifold quotients

Developed a Kontsevich-like matrix model for these theories

Analyzed Dijkgraaf-Vafa type matrix models and quiver gauge theories

Abstract

We study topological and integrable aspects of $\hat{c}=1$ strings. We consider the circle line theories 0A and 0B at particular radii, and the super affine theories at their self-dual radii. We construct their ground rings, identify them with certain quotients of the conifold, and suggest topological B-model descriptions. We consider the partition functions, correlators and Ward identities, and construct a Kontsevich-like matrix model. We then study all these aspects via the topological B-model description. Finally, we analyse the corresponding Dijkgraaf-Vafa type matrix models and quiver gauge theories.