Lecture Notes in Mathematics

Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional

Authors: Keßler, Enno

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  • Provides a detailed introduction to differential geometry on supermanifolds, including bundles, connections and integration
  • Focuses on super Riemann surfaces, supergeometric analogues of Riemann surfaces motivated by theoretical physics
  • Explains the relation between supergeometry and supersymmetry for the superconformal action on super Riemann surfaces
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  • ISBN 978-3-030-13758-8
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この書籍について

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 first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed.

The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformations of the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them.

This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.

著者について

Enno Keßler has studied Mathematics in Leipzig and Rennes. In 2017, he obtained his PhD from the Universität Leipzig while working at the Max-Planck-Institute for Mathematics in the Sciences. His current research interest is in geometry and mathematical physics where he focuses on super Riemann surfaces and their moduli. Besides Mathematics, Enno Keßler is passionate about cycling, open source software and agriculture.

Table of contents (13 chapters)

Table of contents (13 chapters)

書籍の購入

イーブック ¥5,053
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-030-13758-8
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: EPUB, PDF
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
  • ご購入後、すぐにダウンロードしていただけます。
ソフトカバー ¥6,317
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-030-13757-1
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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書誌情報

Bibliographic Information
Book Title
Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2230
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
イーブック ISBN
978-3-030-13758-8
DOI
10.1007/978-3-030-13758-8
ソフトカバー ISBN
978-3-030-13757-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 305
Number of Illustrations
51 b/w illustrations
Topics

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