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

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.