Calabi-Yau Duals of Torus Orientifolds

TL;DR

This paper explores a duality linking a specific orientifold with flux to Calabi-Yau compactifications, revealing that the resulting Calabi-Yau manifolds are abelian surface fibrations with detailed geometric properties.

Contribution

It demonstrates a duality between flux compactifications and Calabi-Yau manifolds, explicitly characterizing the geometry and symmetries of the dual Calabi-Yau threefolds.

Findings

Calabi-Yau manifolds are abelian surface (T^4) fibrations over P^1.

Computed Hodge numbers, intersection numbers, and isometries of the threefolds.

S-duality maps to T-duality of the fibers in the dual description.

Abstract

We study a duality that relates the T^6/Z_2 orientifold with N=2 flux to standard fluxless Calabi-Yau compactifications of type IIA string theory. Using the duality map, we show that the Calabi-Yau manifolds that arise are abelian surface (T^4) fibrations over P^1. We compute a variety of properties of these threefolds, including Hodge numbers, intersection numbers, discrete isometries, and H_1(X,Z). In addition, we show that S-duality in the orientifold description becomes T-duality of the abelian surface fibers in the dual Calabi-Yau description. The analysis is facilitated by the existence of an explicit Calabi-Yau metric on an open subset of the geometry that becomes an arbitrarily good approximation to the actual metric (at most points) in the limit that the fiber is much smaller than the base.