Complex/Symplectic Mirrors

TL;DR

This paper constructs new classes of non-Kaehler string theory vacua with symplectic and complex structures, providing evidence for mirror symmetry and suggesting a broader geometric landscape connecting different manifold classes.

Contribution

It introduces a novel class of symplectic and complex non-Kaehler string vacua and demonstrates their mirror pairing, extending previous theoretical frameworks.

Findings

Constructed symplectic non-Kaehler string vacua

Established mirror pairing for these vacua

Suggested a geometric extension of Reid's fantasy

Abstract

We construct a class of symplectic non--Kaehler and complex non--Kaehler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger. The class admits a mirror pairing by construction. Comparing hints from a variety of sources, including ten--dimensional supergravity and KK reduction on SU(3)--structure manifolds, suggests a picture in which string theory extends Reid's fantasy to connect classes of both complex non-Kaehler and symplectic non-Kaehler manifolds.