Edoardo Lauria - N = 2 Supergravity in D = 4, 5, 6 Dimensions

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Supergravity theories play an important role in present-day research on fundamental interactions. A profound knowledge can only be gained by understanding how supergravity theories are constructed. To understand the necessary techniques is not easy starting from the published literature. Despite the presence of a few books, it turns out that a detailed explanation is still lacking and this is particularly the case for supergravity theories with matter couplings in so-called supergravity. In this book, we want to provide a detailed explanation of these theories and tools that researchers have used to construct supergravity theories with 8 real supercharges, in 4, 5 and 6 dimensions.

The basic technique is the superconformal calculus. We explain these methods from basic principles. Chapter. These geometries go together under the name of special geometries, which include special Khler geometry and quaternionic-Khler manifolds.

For readers who want to progress soon to final results, Chap.gives a shorter account.

The text grew from lecture notes during the semester Supergravity, superstrings and M-theory at Institut Henri Poincar, Paris, in November 2000. Parts of it have been available on internet sites and were appreciated by many researchers. We hope that this book will be useful as well for students as for researchers who want to know how these standard theories are constructed and what is their geometric structure.

The notes for this book received input from many people in our field. We first of all thank Robin De Roover and Gabriele Tartaglino-Mazzucchelli, who collaborated for some time to write this book.

The text is based on several fruitful collaborations on supergravities, and we thank Eric Bergshoeff, Marco Bill, Anna Ceresole, Piet Claus, Frederik Coomans, Ben Craps, Eugne Cremmer, Sorin Cucu, Riccardo DAuria, Gianguido DallAgata, Mees de Roo, Bernard de Wit, Tim de Wit, Jean-Pierre Derendinger, Martijn Derix, Sergio Ferrara, Pietro Fr, Dan Freedman, Jos Gheerardyn, Luciano Girardello, Rein Halbersma, Renata Kallosh, Costas Kounnas, Paul Lauwers, Marin Lled, scar Maci, Roeland Philippe, Tullio Regge, Diederik Roest, Frederik Roose, Jan Rosseel, Ergin Sezgin, Paolo Soriani, S.-Q. Su, Walter Troost, Franois Vanderseypen, Stefan Vandoren, Jan-Willem van Holten, Kor Van Hoof, Veeravalli Varadarajan and Bert Vercnocke who contributed significantly to the content in this book. We thank the many colleagues whose remarks have been helpful to improve the text: Marco Baggio, Nikolay Bobev, Alessio Celi, Jan De Rydt, Alessandra Gnecchi, Dietmar Klemm, Joris Van den Bergh and Marco Zagermann. Special thanks also to Stefan Theisen who encouraged us to write this review.