A long-standing conjecture of Reid states that all SU(3) manifolds, whether CY or not, should lie on a single connected moduli space, with transitions from CY to non-Kahler subspaces controlled by local conifold transitions. In this lecture I will introduce a microscopic description of a special class of Heterotic flux vacua and demonstrate that the moduli space of CY and non-Kahler SU(3) manifolds in this class is smoothly connected on the worldsheet.

MIT