2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/193018In this article, we formulate a planar limited version of the B-side in homological mirror symmetry that formularizes Chern-Simons-type topological open string field theory using homotopy associative algebra ($A_{\infty}$ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We show that our formularization includes gravity/gauge theory correspondence which originates in the AdS/CFT duality of Dijkgraaf-Vafa theory.15 pages, 3 figures. v2: minor corrections, references added, v3: fonts changed, accepted for publication in Int. J. Mod. Phys. AHigh Energy Physics - TheoryAlgebraic GeometrySymplectic Geometrytext