Supergravity, Brane Dynamics and String Duality

Abstract

In this review we show that a Clifford algebra possesses a unique irreducible representation; the spinor representation. We discuss what types of spinors can exist in Minkowski space-times and we explain how to construct all the supersymmetry algebras that contain a given space-time Lie algebra. After deriving the irreducible representations of the superymmetry algebras, we explain how to use them to systematically construct supergravity theories. We give the maximally supersymmetric supergravity theories in ten and eleven dimensions and discuss their properties. We find which superbranes can exist for a given supersymmetry algebra and we give the dynamics of the superbranes that occur in M theory. Finally, we discuss how the properties of supergravity theories and superbranes provide evidence for string duality. In effect, we present a continuous chain of argument that begins with Clifford algebras and leads via supersymmetry algebras and their irreducible representations to supergravity theories, string duality, brane dynamics and M theory.

109 pages, 2 figures, plain tex

References in corpus (2)

• The Dirichlet Super-p-Branes in Ten-Dimensional Type IIA and IIB Supergravity
• D-Brane Actions with Local Kappa Symmetry

Cited by in corpus (19)

• Superbranes and Superembeddings
• Superparticle Models with Tensorial Central Charges
• The geometry of branes and extended superspaces
• Dynamics of Higher Spin Fields and Tensorial Space
• Brane Gases on K3 and Calabi-Yau Manifolds
• N=4 Supersymmetric AdS5 Vacua and their Moduli Spaces
• Brane Dynamics From Non-Linear Realizations
• Clifford algebras and their applications to Lie groups and spinors
• Higher Loop Spin Field Correlators in Various Dimensions
• The Non-Split Scalar Coset in Supergravity Theories
• Massive Supermultiplets in Four-Dimensional Superstring Theory
• On Seven-Brane and Instanton Solutions of Type IIB
• Current Density Distributions and a Supersymmetric Action for Interacting Brane Systems
• On the Symmetric Space Sigma-Model Kinematics
• SOSpin, a C++ library for Yukawa decomposition in SO(2N) models
• The Dirac equation in D-dimensional spherically symmetric spacetimes
• Gelfand-Fuchs cohomology and M-Theory as a Topological Quantum Field Theory
• A new invariant for sigma models
• Supersymmetric Gauge Theories from String Theory