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
11 - Type IIB orientifolds
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 construct orientifolds of type IIB 4d compactifications. There are several constructions in this class, including toroidal orientifolds, systems of D3-branes at singularities, and magnetized D-branes, providing the mirrors of type IIA models in Chapter 10. We also introduce F-theory and its compactifications. These setups provide a rich arena for particle physics model building in string theory.
Generalities of type IIB orientifold actions
Type IIB orientifolds are obtained by considering IIB theory on a CY X6 and modding out by ΩR, where R is a geometric symmetry acting holomorphically on the complex coordinates on X6. For instance, the simplest orientifold action is just Ω, with trivial R, thus acting holomorphically zi → zi in a trivial way. These models involve 10d spacetime filling orientifold planes (O9-planes) and open string sectors (D9-branes), and so correspond to type I compactifications on X6, which are thus included as particular type IIB orientifold compactifications. Additional constructions are obtained for non-trivial actions R, as follows:
• O7/D7 models: Consider the orientifold action ΩRi (–1)FL, where Ri acts as zi →–zi leaving other complex coordinates invariant; the factor (–1)FL, with FL being the leftmoving fermion number, is necessary for the orientifold action to square to the identity operator. The quotient introduces O7-planes at the fixed points of Ri, namely transverse to the coordinate zi, and wrapped on a 4-cycle parametrized by the remaining two complex coordinates.
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- String Theory and Particle PhysicsAn Introduction to String Phenomenology, pp. 340 - 395Publisher: Cambridge University PressPrint publication year: 2012