On the Vacuum Structure of Type II String Compactifications on Calabi-Yau Spaces with H-Fluxes

TL;DR

This paper analyzes how H-fluxes influence the vacuum structure of type II string compactifications on Calabi-Yau spaces, revealing conditions for supersymmetry preservation and connections to supergravity and black hole attractors.

Contribution

It provides a detailed study of the H-flux induced superpotential and scalar potential at various Calabi-Yau degeneration points, exploring supersymmetry breaking and preservation mechanisms.

Findings

H-fluxes lift vacuum degeneracy in Calabi-Yau moduli space.

Supersymmetric vacua can exist at degeneration points with aligned H-flux.

Analogies are drawn between flux vacua and black hole attractor formalism.

Abstract

We discuss the vacuum structure of type IIA/B Calabi-Yau string compactifications to four dimensions in the presence of n-form H-fluxes. These will lift the vacuum degeneracy in the Calabi-Yau moduli space, and for generic points in the moduli space, N=2 supersymmetry will be broken. However, for certain `aligned' choices of the H-flux vector, supersymmetric ground states are possible at the degeneration points of the Calabi-Yau geometry. We will investigate in detail the H-flux induced superpotential and the corresponding scalar potential at several degeneration points, such as the Calabi-Yau large volume limit, the conifold loci, the Seiberg-Witten points, the strong coupling point and the conformal points. Some emphasis is given to the question whether partial supersymmetry breaking can be realized at those points. We also relate the H-flux induced superpotential to the formalism of gauged N=2 supergravity. Finally we point out the analogies between the Calabi-Yau vacuum structure due to H-fluxes and the attractor formalism of N=2 black holes.