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

G. Curio, A. Klemm, D. Luest, S. Theisen

TL;DR

The paper analyzes how internal H-fluxes in Type II string compactifications on Calabi–Yau manifolds lift moduli and typically break N=2 supersymmetry, while aligned fluxes can produce supersymmetric vacua at Calabi–Yau degeneration points. It develops a unified framework in terms of a symplectic, gauged N=2 supergravity description, with a flux-induced superpotential W = ⟨H,Ξ⟩ that can be expressed in terms of period vectors and their duals, and it connects this to the attractor mechanism of N=2 black holes. The authors perform a detailed survey of degeneration points (large volume, conifold, Seiberg–Witten, strong coupling, conformal) in both IIB and IIA pictures, identifying when SUSY vacua can arise and when the scalar potential is minimized, often via attractor-like dynamics. They also show how including NS fluxes can alter the vacuum structure, potentially yielding fully N=2 vacua at finite moduli, and discuss the broader implications for dualities and geometric engineering.

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.

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

TL;DR

The paper analyzes how internal H-fluxes in Type II string compactifications on Calabi–Yau manifolds lift moduli and typically break N=2 supersymmetry, while aligned fluxes can produce supersymmetric vacua at Calabi–Yau degeneration points. It develops a unified framework in terms of a symplectic, gauged N=2 supergravity description, with a flux-induced superpotential W = ⟨H,Ξ⟩ that can be expressed in terms of period vectors and their duals, and it connects this to the attractor mechanism of N=2 black holes. The authors perform a detailed survey of degeneration points (large volume, conifold, Seiberg–Witten, strong coupling, conformal) in both IIB and IIA pictures, identifying when SUSY vacua can arise and when the scalar potential is minimized, often via attractor-like dynamics. They also show how including NS fluxes can alter the vacuum structure, potentially yielding fully N=2 vacua at finite moduli, and discuss the broader implications for dualities and geometric engineering.

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.

Paper Structure

This paper contains 27 sections, 156 equations.

Table of Contents

  1. Introduction
  2. The superpotential from H-fluxes
  3. Special geometry and vector couplings
  4. Hypermultiplet Couplings and superpotential
  5. Gauged ${\cal N}=2$ supergravity
  6. Symplectic covariance
  7. The ground state of the theory -- the question of partial supersymmetry breaking
  8. The superpotential from type IIB 3-form Fluxes
  9. Calabi-Yau compactification
  10. The scalar potential and the question of partial supersymmetry breaking
  11. The type IIB superpotential from gauged ${\cal N}=2$ supergravity
  12. The superpotential from type IIA fluxes
  13. Relation between the superpotential due to Ramond fluxes and ${\cal N}=2$ black holes and attractor mechanism
  14. Type II Vacua with Ramond Fluxes
  15. Type II compactifications on Calabi-Yau threefolds
  16. ...and 12 more sections