Book contents
- Frontmatter
- Contents
- Preface
- 1 The Standard Model and beyond
- 2 Supersymmetry
- 3 Introduction to string theory: the bosonic string
- 4 Superstrings
- 5 Toroidal compactification of superstrings
- 6 Branes and string duality
- 7 Calabi–Yau compactification of heterotic superstrings
- 8 Heterotic string orbifolds and other exact CFT constructions
- 9 Heterotic string compactifications: effective action
- 10 Type IIA orientifolds: intersecting brane worlds
- 11 Type IIB orientifolds
- 12 Type II compactifications: effective action
- 13 String instantons and effective field theory
- 14 Flux compatifications and moduli stabilization
- 15 Moduli stabilization and supersymmetry breaking in string theory
- 16 Further phenomenological properties. Strings and cosmology
- 17 The space of string vacua
- Appendix A Modular functions
- Appendix B Some topological tools
- Appendix C Spectrum and charges of a semi-realistic Z3 heterotic orbifold
- Appendix D Computation of RR tadpoles
- Appendix E CFT toolkit
- Bibliography
- References
- Index
14 - Flux compatifications and moduli stabilization
Published online by Cambridge University Press: 05 March 2012
- Frontmatter
- Contents
- Preface
- 1 The Standard Model and beyond
- 2 Supersymmetry
- 3 Introduction to string theory: the bosonic string
- 4 Superstrings
- 5 Toroidal compactification of superstrings
- 6 Branes and string duality
- 7 Calabi–Yau compactification of heterotic superstrings
- 8 Heterotic string orbifolds and other exact CFT constructions
- 9 Heterotic string compactifications: effective action
- 10 Type IIA orientifolds: intersecting brane worlds
- 11 Type IIB orientifolds
- 12 Type II compactifications: effective action
- 13 String instantons and effective field theory
- 14 Flux compatifications and moduli stabilization
- 15 Moduli stabilization and supersymmetry breaking in string theory
- 16 Further phenomenological properties. Strings and cosmology
- 17 The space of string vacua
- Appendix A Modular functions
- Appendix B Some topological tools
- Appendix C Spectrum and charges of a semi-realistic Z3 heterotic orbifold
- Appendix D Computation of RR tadpoles
- Appendix E CFT toolkit
- Bibliography
- References
- Index
Summary
In all string compactifications studied in previous chapters, the massless spectrum contains a large number of moduli, including the dilaton and the CY geometric moduli. These are problematic, as they couple to matter particles and easily lead to deviations from universality of gravitational interactions (fifth forces), which have not been observed experimentally. Therefore, any serious attempt to reproduce realistic string models of particle physics and/or cosmology, must address the issue of moduli stabilization; namely, the generation of a scalar potential fixing the vevs of the moduli fields and giving them large enough masses to overcome such phenomenological problems. In this chapter we review a very general and systematic mechanism to fix large numbers of (or even all) moduli. It is based on a generalization of the simplest compactification ansatz, allowing for non-trivial backgrounds for additional 10d fields. Most prominently, the compactifications include non-trivial fluxes for the field strength tensor of the diverse p-form fields in the 10d theory. Application of string dualities to these motivates additional possible backgrounds, termed geometric and non-geometric fluxes. Compactifications including field strength fluxes, or their generalizations, are thus known as “flux compactifications.” This chapter focuses on their definition and impact on moduli stabilization, while their role in SUSY breaking is further explored in Chapter 15.
Type IIB with 3-form fluxes
A prototypical class of flux compactifications is obtained from type IIB (orientifolds) on CY geometries with non-trivial fluxes for the NSNS and RR 3-form field strengths (and their F-theory generalization, which we briefly touch upon).
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- String Theory and Particle PhysicsAn Introduction to String Phenomenology, pp. 455 - 482Publisher: Cambridge University PressPrint publication year: 2012