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
6 - Branes and string duality
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
We have studied the main properties of string theory in the framework of perturbation theory. However, on physical grounds we expect the theory to have interesting non-perturbative dynamics; for instance, because the low-energy limit of string theory contains gauge theories, which do have non-perturbative effects. Although a complete definition of string theory at the non-perturbative level is lacking, there is a considerable body of knowledge on some of its properties. In this chapter we introduce certain non-perturbative extended states known as branes, and review their role in non-perturbative string theory and in string duality.
D-branes in string theory
We start by uncovering the existence in string theory of certain non-perturbative states which admit a remarkably simple description. They are the Dp-branes, extended objects of p spatial dimensions, which at weak coupling can be defined as (p + 1)-dimensional subspaces of spacetime on which open strings end. They are crucial in the study of nonperturbative dualities in string theory, but also in the construction of string compactifications, as exploited in Chapters 10 and 11. In fact, we have already encountered D-branes in the orientifold compactification of Section 5.3.
D-branes as non-perturbative states
In Section 5.3.4 we described compatifications of type IIA or IIB string theory with sectors of open strings ending on certain lower-dimensional planes, the D-branes. In fact, these D-branes already exist in the theory in flat 10d spacetime, as can be recovered by taking a suitable decompactification limit.
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- Information
- String Theory and Particle PhysicsAn Introduction to String Phenomenology, pp. 155 - 184Publisher: Cambridge University PressPrint publication year: 2012