Supersolutions

TL;DR

This paper systematically develops classical supersymmetric theories across various dimensions and supersymmetry levels, emphasizing geometric aspects and providing detailed computations in both component and superspace formalisms.

Contribution

It offers a unified treatment of supersymmetric theories in multiple dimensions and supersymmetry amounts, with detailed calculations and geometric insights, in a comprehensive two-volume work.

Findings

Explicit lagrangian computations for various supersymmetric theories

Unified geometric framework for supersymmetry across dimensions

Detailed discussion of superspace and component formalisms

Abstract

We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we emphasize geometric aspects. The beginning chapters give a general discussion about supersymmetric field theories; then we move on to detailed computations of lagrangians, etc. in specific theories. An appendix details our sign conventions. This text will appear in a two-volume work "Quantum Fields and Strings: A Course for Mathematicians" to be published soon by the American Mathematical Society. Some of the cross-references may be found at http://www.math.ias.edu/~drm/QFT/