Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional

• Main Author: Keßler, Enno (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Lecture Notes in Mathematics, 2230
• Subjects: Differential geometry.; Mathematical physics.; Quantum field theory.; String theory.; Differential Geometry.; Mathematical Physics.; Quantum Field Theories, String Theory.

This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry. The objective is to understand its symmetries as geometric properties of super Riemann surfaces, which are particular complex super manifolds of dimension 1|1. The fir...

Table of Contents:

• Introduction
• PART I Super Differential Geometry
• Linear Superalgebra
• Supermanifolds
• Vector Bundles
• Super Lie Groups
• Principal Fiber Bundles
• Complex Supermanifolds
• Integration
• PART II Super Riemann Surfaces
• Super Riemann Surfaces and Reductions of the Structure Group
• Connections on Super Riemann Surfaces
• Metrics and Gravitinos
• The Superconformal Action Functional
• Computations in Wess-Zumino Gauge.