Book contents
- Frontmatter
- Dedication
- Contents
- Introduction
- 1 Free field theory with boundaries
- 2 Superstrings and branes
- 3 Conformal field theory on the plane
- 4 Boundary conformal field theory
- 5 Perturbations of boundary conformal field theories
- 6 The Wess–Zumino–Witten model on SU(2)
- 7 Gepner model boundary states and Calabi–Yau branes
- Appendix
- References
- Index
1 - Free field theory with boundaries
Published online by Cambridge University Press: 05 November 2013
- Frontmatter
- Dedication
- Contents
- Introduction
- 1 Free field theory with boundaries
- 2 Superstrings and branes
- 3 Conformal field theory on the plane
- 4 Boundary conformal field theory
- 5 Perturbations of boundary conformal field theories
- 6 The Wess–Zumino–Witten model on SU(2)
- 7 Gepner model boundary states and Calabi–Yau branes
- Appendix
- References
- Index
Summary
Our aim in the first chapter is to explain the microscopic theory of strings and branes in flat backgrounds. The corresponding two-dimensional worldsheet theories can be solved with elementary methods. This will not only give us a chance to meet most of the relevant quantities from two-dimensional field theory but also to pass from worldsheet to target space concepts without much technical struggle.
Our exposition begins with an analysis of free bosonic fields on the half-plane. After a few comments on the classical action and possible boundary conditions we shall solve the model. The solution will enable us to calculate bulk operator products and correlation functions. Moreover, we shall take a first look at a few central concepts, such as gluing conditions, boundary states, bulk and boundary fields and operator products. Once free bosonic fields are dealt with, we shall perform a similar analysis for fermions. Throughout the entire chapter, some familiarity with free field theory on the complex plane will be assumed.
Free bosonic field theory
This section is devoted to the simplest two-dimensional Euclidean quantum field theory, namely a theory of free bosons. Since the model is easily solved, it allows an unobstructed approach to the main features of conformal field theory (CFT) in the presence of boundaries. The choice of boundary conditions has many interesting consequences. For example, it influences the correlation functions of bulk fields, i.e. of fields that are inserted at points in the interior of the worldsheet.
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- Publisher: Cambridge University PressPrint publication year: 2013