Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 A Brief History of Unification
- 2 Gravitation
- 3 Non-abelian Gauge Theory
- 4 Spontaneous Breaking of Global and Local Symmetries
- 5 The Standard Model
- 6 Anomalies
- 7 Effective Lagrangians
- 8 Supersymmetry
- 9 Grand Unification
- 10 The MSSM Lagrangian
- 11 N = 1 Supergravity
- 12 Coupling of Supergravity with Matter and Gauge Fields
- 13 Supergravity Grand Unification
- 14 Phenomenology of Supergravity Grand Unification
- 15 CP Violation in Supergravity Unified Theories
- 16 Proton Stability in Supergravity Unified Theories
- 17 Cosmology, Astroparticle Physics, and Supergravity Unification
- 18 Extended Supergravities and Supergravities from Superstrings
- 19 Specialized Topics
- 20 The Future of Unification
- 21 Appendices
- 22 Notation, Conventions, and Formulae
- 23 Constants and Units
- 24 Further Reading
- Author Index
- Subject Index
- References
18 - Extended Supergravities and Supergravities from Superstrings
Published online by Cambridge University Press: 30 December 2016
- Frontmatter
- Dedication
- Contents
- Preface
- 1 A Brief History of Unification
- 2 Gravitation
- 3 Non-abelian Gauge Theory
- 4 Spontaneous Breaking of Global and Local Symmetries
- 5 The Standard Model
- 6 Anomalies
- 7 Effective Lagrangians
- 8 Supersymmetry
- 9 Grand Unification
- 10 The MSSM Lagrangian
- 11 N = 1 Supergravity
- 12 Coupling of Supergravity with Matter and Gauge Fields
- 13 Supergravity Grand Unification
- 14 Phenomenology of Supergravity Grand Unification
- 15 CP Violation in Supergravity Unified Theories
- 16 Proton Stability in Supergravity Unified Theories
- 17 Cosmology, Astroparticle Physics, and Supergravity Unification
- 18 Extended Supergravities and Supergravities from Superstrings
- 19 Specialized Topics
- 20 The Future of Unification
- 21 Appendices
- 22 Notation, Conventions, and Formulae
- 23 Constants and Units
- 24 Further Reading
- Author Index
- Subject Index
- References
Summary
So far we have discussed N = 1 supergravity theory in four dimensions. However, one may formulate supergravity for larger values of N in four dimensions, and some of the interesting cases are for N = 2, 4, and 8. The particle content of the supergravity multiplet for these cases is
• N = 2: graviton (1), gravitino (2), vector (1);
• N = 4: graviton (1), gravitino (4), vector (6), spin 1/2 (4), spin 0 (1);
• N = 8: graviton (1), gravitino (8), vector (28), spin 1/2 (56), spin 0 (70).
Thus, the supergravity multiplet for the case N = 2 consists of the graviton field, two spin 3/2 gravitini, and one vector field. One can think of the N = 2 as consisting of two N = 1 multiplets, one of which is the graviton multiplet consisting of spin 2 and spin 3/2 and the other, which is the gravitino multiplet, consisting of spin 3/2 and spin 1. Thus, one way to look at the N = 2 supergravity multiplet is to think of coupling the gravitino multiplet consisting of spin 3/2 and spin 1 to N = 1 supergravity, which results in N = 2 local supersymmetry. N = 8 is the supergravity with the largest value of N. For N > 8, one will get helicity states larger than two for which consistent interacting local theories cannot be formulated At one time, the N = 8 supergravity theory was thought to be the ultimate unified theory until it was noted that the group SO(8) does not accommodate the weak group SU(2)w. One way of obtaining supergravity theories in four dimensions with higher N is to consider supergravity theories in higher dimensions and carry out a dimensional reduction or compactification to lower dimensions. Thus, the N = 8 theory can be shown to arise from compactification of 11-dimensional supergravity on a seven-dimensional torus T7 [3]. We discuss supergravity theories formulated in higher dimensions below.
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- Supersymmetry, Supergravity, and Unification , pp. 404 - 427Publisher: Cambridge University PressPrint publication year: 2016