Supergravity, Brane Dynamics and String Duality

TL;DR

This review explores the mathematical foundations of supergravity, superbranes, and string duality, illustrating how Clifford algebras and supersymmetry inform the understanding of M theory and related high-dimensional theories.

Contribution

It systematically constructs supergravity theories from Clifford algebras and supersymmetry algebras, linking algebraic structures to physical theories like M theory and string duality.

Findings

Maximally supersymmetric supergravity theories in 10 and 11 dimensions identified

Classification of superbranes compatible with supersymmetry algebras provided

Evidence for string duality derived from supergravity and superbrane properties

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.