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
9 - Heterotic string compactifications: effective action
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 this chapter we consider different aspects of the low-energy 4d effective action of heterotic compactifications. After discussing the structure of the effective action for the general CY compactifications of Chapter 7, we concentrate on the case of the abelian orbifold compactifications of Chapter 8, in which several additional aspects can be described in an explicit quantitative fashion. We discuss the form of the Kähler potential and the superpotential, as well as the gauge kinetic function and their one-loop corrections. In toroidal orbifolds the low-energy effective actionmust bemodular invariant under T-duality transformations, and this leads to strong constraints on its structure. A general feature of heterotic compactifications is that they often have a non-trivial cancellation of mixed U(1) anomalies, involving a generalized Green×Schwarz mechanism. This renders some U(1) gauge bosons massive, and introduces a one-loop re-stabilization of the vacuum, triggering the breaking of extra gauge symmetries and the disappearance of charged matter multiplets. This phenomenon can be efficiently exploited in the construction of improved models of particle physics, as we describe using explicit examples.
A first look at the heterotic 4d N =1 effective action
We start by motivating the general structure of the effective action of heterotic string geometric (CY or orbifold) compactifications by using an intuitive description of the truncation to the zero mode sector. The resulting structure is quite general, as can be shown to largely follow from symmetries of the system. We finally describe more explicit results for CY compactifications with standard embedding.
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- Information
- String Theory and Particle PhysicsAn Introduction to String Phenomenology, pp. 264 - 297Publisher: Cambridge University PressPrint publication year: 2012