Basics of M-Theory

TL;DR

This review article provides detailed calculations and explanations of eleven-dimensional supergravity, covering fundamental equations, solutions, and mathematical tools like Clifford algebras, aimed at researchers and students in theoretical physics.

Contribution

It offers a comprehensive, step-by-step presentation of supergravity calculations and solutions, including detailed derivations and explanations, serving as a valuable resource for understanding M-theory.

Findings

Explicit derivation of equations of motion including fermions

Construction of simple supersymmetric solutions

Detailed methodology for calculations in supergravity

Abstract

This is a review article of eleven dimensional supergravity in which we present all necessary calculations, namely the Noether procedure, the equations of motion (without neglecting the fermions), the Killing spinor equation, as well as some simple and less simple supersymmetric solutions to this theory. All calculations are printed in much detail and with explicit comments as to how they were done. Also contained is a simple approach to Clifford algebras to prepare the grounds for the harder calculations in spin space and Fierz identities.