Supermanifolds - Theory and Applications

Abstract

This book aims to fill the gap in the literature available on supermanifolds. In two sections, the book describes the different approaches to supermanifolds, with applications to physics, including some which rely on the more mathematical aspects of supermanifold theory. The first part of the book contains a full introduction to the theory of supermanifolds, comparing and contrasting the different approaches that exist. This section includes tensor calculus on supermanifolds, supervector bundles, superlie groups and integration theory. The second part emphasizes applications. It begins with a review of supersymmetry and a treatment of various supersymmetric theories in flat superspace, in particular supersymmetric Yang-Mills theories. It continues with supergravity theories in various dimensions and their associated supermanifold formulations. Included is a discussion of harmonic superspace. The final topic is super-Riemann surfaces, their geometry and their role in string theory.