Geometric Dual and Matrix Theory for $SO/Sp$ Gauge Theories

TL;DR

This paper proves the equivalence between certain supersymmetric $SO/Sp$ gauge theories, their dual string theory descriptions, and matrix models, establishing a unified geometric and algebraic framework.

Contribution

It demonstrates the equivalence of ${ m extbf{N}=1}$ $SO/Sp$ gauge theories, dual string theories, and matrix models through geometric transition and duality arguments.

Findings

Proves the equivalence of gauge theories and string duals.

Establishes the connection between geometric transition and matrix models.

Provides a unified framework for understanding $SO/Sp$ gauge theories.

Abstract

In this paper, we give a proof of the equivalence of ${\cal N}=1$ $SO/Sp$ gauge theories deformed from ${\cal N}=2$ by the superpotential of adjoint field $\Phi$, the dual type IIB superstring theory on CY threefold geometries with fluxes and orientifold action after geometric transition. Furthermore, by relating the geometric picture to the matrix model, we show the equivalence between the field theory and the corresponding matrix model.