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
13 - Supergravity theories in four, ten and eleven dimensions
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
I was at first almost frightened when I saw such mathematical force made to bear upon the subject, and then wondered to see the subject stood it so well.
FaradayWe take a supergravity theory to be one that has some supersymmetry and contains gravity, but no higher spin fields. In ten and eleven dimensions, there exist only four supergravity theories which are distinguished by their different underlying supersymmetry algebras. The types of spinor one can have in different dimensions was studied in chapter 5 and it is key to understanding the different possible supersymmetry algebras. In turn, the number of components of the supercharge determines the number of degrees of freedom and the spins of the particles in the supermultiplet. By analysing the irreducible representations of supersymmetry algebras in general dimensions it was shown [10.10] than there is only one supersymmetry multiplet in eleven dimensions containing no spin higher than gravity, no such multiplets above eleven dimensions and only four such supermultiplets in ten dimensions. A Majorana spinor in ten and eleven dimensions has 32 = 210/2 components. In eleven dimensions there is only one supergravity theory [13.1] whose supersymmetry algebra contains a supercharge which is a Majorana spinor. In ten dimensions we can have Majorana–Weyl spinors, which have 16 components. In this dimension there are two maximal supergravity theories: the IIA supergravity theory [10.11–10.13] which has a supersymmetry algebra with one Majorana spinor and so two Majorana–Weyl spinors of opposite chirality, and the IIB supergravity theory [10.14–10.16], which contains a supersymmetry algebra with two Majorana-Weyl spinors of the same chirality.
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- Chapter
- Information
- Introduction to Strings and Branes , pp. 320 - 419Publisher: Cambridge University PressPrint publication year: 2012