TL;DR
This paper formulates a planar version of the B-side in homological mirror symmetry, connecting topological string theory with gravity/gauge duality through homotopy algebra.
Contribution
It introduces a novel planar formulation of homological mirror symmetry's B-side using $A_{ abla}$ algebra, linking to Dijkgraaf-Vafa theory and AdS/CFT duality.
Findings
Includes gravity/gauge theory correspondence in the formulation.
Connects homological mirror symmetry with topological string field theory.
Provides a mathematical framework for dualities in string theory.
Abstract
In 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 ( 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.
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