Book contents
- Frontmatter
- Contents
- Preface
- 1 The point particle
- 2 The classical bosonic string
- 3 The quantum bosonic string
- 4 The light-cone approach
- 5 Clifford algebras and spinors
- 6 The classical superstring
- 7 The quantum superstring
- 8 Conformal symmetry and two-dimensional field theory
- 9 Conformal symmetry and string theory
- 10 String compactification and the heterotic string
- 11 The physical states and the no-ghost theorem
- 12 Gauge covariant string theory
- 13 Supergravity theories in four, ten and eleven dimensions
- 14 Brane dynamics
- 15 D-branes
- 16 String theory and Lie algebras
- 17 Symmetries of string theory
- 18 String interactions
- Appendix A The Dirac and BRST methods of quantisation
- Appendix B Two-dimensional light-cone and spinor conventions
- Appendix C The relationship between S2 and the Riemann sphere
- Appendix D Some properties of the classical Lie algebras
- Chapter quote acknowledgements
- References
- Index
10 - String compactification and the heterotic string
Published online by Cambridge University Press: 05 November 2012
- Frontmatter
- Contents
- Preface
- 1 The point particle
- 2 The classical bosonic string
- 3 The quantum bosonic string
- 4 The light-cone approach
- 5 Clifford algebras and spinors
- 6 The classical superstring
- 7 The quantum superstring
- 8 Conformal symmetry and two-dimensional field theory
- 9 Conformal symmetry and string theory
- 10 String compactification and the heterotic string
- 11 The physical states and the no-ghost theorem
- 12 Gauge covariant string theory
- 13 Supergravity theories in four, ten and eleven dimensions
- 14 Brane dynamics
- 15 D-branes
- 16 String theory and Lie algebras
- 17 Symmetries of string theory
- 18 String interactions
- Appendix A The Dirac and BRST methods of quantisation
- Appendix B Two-dimensional light-cone and spinor conventions
- Appendix C The relationship between S2 and the Riemann sphere
- Appendix D Some properties of the classical Lie algebras
- Chapter quote acknowledgements
- References
- Index
Summary
But all these four Muses (Bach, Handel, Gluck, and Haydon) are amalgamated in Mozart. He who knows Mozart also knows what is good in these four, because being the greatest and most potent of all musical creators, he was not adverse, even, to taking them under his wings and saving them from oblivion. They are rays lost in the sun of Mozart.
Tchaikovsky 1886In this chapter we consider the dimensional reduction of a closed bosonic string on a torus. The string is an extended object and this leads to some important differences in its dimensional reduction compared to that for a point particle. One of the main differences is that the string can wind itself around the torus leading to an enlarged set of states. The resulting compactified string possesses some unexpected symmetries. We also consider constructions for which the left and right moving modes on the world sheet of the string are treated independently and belong to different tori.
These discussions naturally motivate the construction of the heterotic string in the final section.
Compactification on a circle
Let us consider the closed bosonic string moving in a space-time in which one dimension, with coordinate, say x25, is a circle of radius R. Its dynamics is determined by the same actions as given in chapter 2. As we have a closed string we must consider the possibility that the string can wind itself around the circle [10.1].
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- Chapter
- Information
- Introduction to Strings and Branes , pp. 240 - 271Publisher: Cambridge University PressPrint publication year: 2012