Duality and statistical mirror symmetry in the generalized geometry setting

Abstract

We describe statistical mirror symmetry, we introduce the notion of quasi-statistical mirror pairs and we give examples for certain quasi-statistical manifolds. As an application, we get families of almost Kahler structures on the tangent bundle manifold of almost complex $4$-dimensional solvmanifolds without complex structures. Finally, we prove that statistical mirror symmetry can be understood in terms of generalized geometry.