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
12 - Gauge covariant string theory
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
First they told me it was wrong, then they told me it was obvious.
Murray Gell-MannIn this chapter we will formulate the free bosonic string and superstrings as a field theories in their critical dimensions in a way that manifestly possesses Lorentz invariance. While it is to be expected that these theories possess the gauge symmetries of the massless modes we will find that such a formulation of string theory possesses an infinite number of local symmetries. The actions have considerable elegance and make a surprising use of the BRST formalism even though they are classical objects.
One of the most remarkable aspects of the evolution of modern physics has been the central role played by symmetry. Themost important are local symmetries which place very strong constraints on the form of the theory that possesses them. This first discovery of a gauge symmetry was by Weyl in the electromagnetic equations of Maxwell and continued in the construction of the Standard Model which possesses the SU(3) ⊗ SU(2) ⊗ U(1) gauge symmetry. Another crucial tool which played an important role in modern physics is the Feynman path integral description of quantum field theory. This formulation possesses the advantage that it is constructed from an action which can be used to manifestly display the symmetries of interest and, as a result, one can more easily derive those properties of the theory which are a consequence of its symmetries.
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- Introduction to Strings and Branes , pp. 293 - 319Publisher: Cambridge University PressPrint publication year: 2012