Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional
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 comp
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Enno Keßler
Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Editors: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Cambridge Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
2230
More information about this series at http://www.springer.com/series/304
Enno Keßler
Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional
123
Enno Keßler Max-Planck-Institut für Mathematik in den Naturwissenschaften Leipzig, Germany
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-030-13757-1 ISBN 978-3-030-13758-8 (eBook) https://doi.org/10.1007/978-3-030-13758-8 Mathematics Subject Classification (2010): Primary: 58A50; Secondary: 32C11, 17C70, 81T60, 83E30 © The Author(s) 2019 This work is subject to copyright. All rights are reserved by the Author, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book grew out of my dissertation thesis accepted by the Universität Leipzig in early 2017. For the book at hand, I have rewritten and expanded several chapters. The leading question for the thesis was how the action functional of the twodimensional non-linear supersymmetric sigma model, or spinning string, is related to the geometry of super Riemann surfaces. The necessary tools from supergeometry to answer that question were quite spread out in the literature or did not exist. It was necessary to gather results from quite diverse places in the literature and reformulate them in a common language and fill in the remaining gaps. Hence the result
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