© 2014

Introduction to Supergravity


  • This book is a pedagogical introduction to supergravity for graduate students and non-expert researchers

  • Supergravities in four and higher dimensional spacetime are discussed from a standpoint of superstring theory

  • Non-compact symmetries of supergravity including electro-magnetic duality symmetries are discussed in detail


Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 1)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Yoshiaki Tanii
    Pages 1-15
  3. Yoshiaki Tanii
    Pages 17-35
  4. Yoshiaki Tanii
    Pages 37-52
  5. Yoshiaki Tanii
    Pages 53-69
  6. Yoshiaki Tanii
    Pages 89-109
  7. Yoshiaki Tanii
    Pages 111-120
  8. Back Matter
    Pages 121-130

About this book


This book is a pedagogical introduction to supergravity, a gravitational field theory that includes supersymmetry (symmetry between bosons and fermions) and is a generalization of Einstein's general relativity. Supergravity provides a low-energy effective theory of superstring theory, which has attracted much attention as a candidate for the unified theory of fundamental particles, and it is a useful tool for studying non-perturbative properties of superstring theory such as D-branes and string duality.

This work considers classical supergravities in four and higher spacetime dimensions with their applications to superstring theory in mind. More concretely, it discusses classical Lagrangians (or field equations) and symmetry properties of supergravities. Besides local symmetries, supergravities often have global non-compact symmetries, which play a crucial role in their applications to superstring theory. One of the main features of this book is its detailed discussion of these non-compact symmetries.

The aim of the book is twofold. One is to explain the basic ideas of supergravity to those who are not familiar with it. Toward that end, the discussions are made both pedagogical and concrete by stating equations explicitly. The other is to collect relevant formulae in one place so as to be useful for applications to string theory.

The subjects discussed in this book include the vielbein formulation of gravity, supergravities in four dimensions, possible types of spinors in various dimensions, superalgebras and supermultiplets, non-linear sigma models for non-compact Lie groups, electric-magnetic duality symmetries, supergravities in higher dimensions, dimensional reductions, and gauged and massive supergravities.


Field theory Gravity Non-compact symmetry Superstring Supersymmetry

Authors and affiliations

  1. 1.Graduate School of Science and EngineeringSaitama UniversitySaitamaJapan

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From the book reviews:

“This small book offers a very good introduction to the mathematical foundations of supergravity. It is a graduate level text, ideal for independent study. … Useful formulae related to gamma matrices and spinors in general dimensions are collected in an appendix at the end of the book. This text will be valuable to anyone teaching or studying supergravities.” (C. Gauthier, Mathematical Reviews, February, 2015)