Mirror symmetry & supersymmetry on SU(4)-structure backgrounds

TL;DR

This paper explores type IIB string theory backgrounds with SU(4)-structure, analyzing complex and symplectic geometries via generalized complex geometry, and proposes a T-duality inspired mirror map extending to non-Kähler geometries.

Contribution

It introduces a map relating complex and symplectic supersymmetric systems on SU(4)-structure backgrounds, extending mirror symmetry concepts to non-Kähler geometries.

Findings

Identification of a map relating complex and symplectic solutions.

Extension of mirror symmetry via T-duality to non-Kähler geometries.

Framework for understanding supersymmetric backgrounds with SU(4)-structure.

Abstract

We revisit the backgrounds of type IIB on manifolds with $SU(4)$-structure and discuss two sets of solutions arising from internal geometries that are complex and symplectic respectively. Both can be realized in terms of generalized complex geometry. We identify a map which relates the complex and symplectic supersymmetric systems. In the semi-flat torus bundle setting this map corresponds to T-duality and suggest a way of extending the mirror transform to non-K\"ahler geometries.