2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202751We show how a recently proposed large $N$ duality in the context of type IIA strings with ${\cal N}=1$ supersymmetry in 4 dimensions can be derived from purely geometric considerations by embedding type IIA strings in M-theory. The phase structure of M-theory on $G_2$ holonomy manifolds and an $S^3$ flop are the key ingredients in this derivation.17 pages, references added and correctedHigh Energy Physics - Theorytext