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F theory Vacua in Four Dimensions and Toric Threefolds

Kenji Mohri

Abstract

We investigate D=4, N=1 F theory models realized by type IIB string compactification on toric threefolds. Massless spectra, gauge symmetries, phase transitions associated with divisor contractions and flops, and non-perturbative superpotentials are analyzed using elementary toric methods.

F theory Vacua in Four Dimensions and Toric Threefolds

Abstract

We investigate D=4, N=1 F theory models realized by type IIB string compactification on toric threefolds. Massless spectra, gauge symmetries, phase transitions associated with divisor contractions and flops, and non-perturbative superpotentials are analyzed using elementary toric methods.

Paper Structure

This paper contains 25 sections, 72 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. D=4 Compactification of F Theory
  3. Toric Threefold and Elliptic Calabi-Yau Fourfold
  4. Spectrum
  5. Spectrum of Toric Hypersurface
  6. Smooth Models
  7. Smooth Elliptic Calabi-Yau Fourfolds
  8. Phase Structure of ${\frak F}_{12}$
  9. Toric Fano Threefolds
  10. Quantum Numbers of Toric Fano Models
  11. Other Smooth Models
  12. ${\Bbb P}^{1}$ bundle over ${\Bbb P}^{2}$ models
  13. Model
  14. ${\Bbb G}_{n}/{\Bbb G}_{n+1}$ Transition
  15. Flop Transitions
  16. ...and 10 more sections

Figures (7)

  • Figure 1: Phase Diagram of ${\frak F}_{12}$ Model
  • Figure 2: Toric Fano Threefolds
  • Figure 3: Fan of ${\cal T}$
  • Figure 4: Flop Transition
  • Figure 5: Phase Diagram of ${\Bbb H}_{n}$ Model
  • ...and 2 more figures