Strings And Geometry: Proceedings Of The Clay Mathematics Institute 2002 Summer School On Strings And Geometry, Isaac Newton Institute, Camb (clay Mathematics Proceedings)

CMIP/3 www.ams.org www.claymath.org 4-color process Douglas, Gauntlett and Gross, Editors This volume contains a selection of expository and research articles by lecturers at the school, and highlights some of the current interests of researchers working at the interface between string theory and algebraic geometry. The topics covered include manifolds of special holonomy, supergravity, supersymmetry, D-branes, the McKay correspondence and the Fourier-Mukai transform. 3 Strings and Geometry This volume is the proceedings of the 2002 Clay Mathematics Institute School on Geometry and String Theory. This month-long program was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, and was organized by both mathematicians and physicists: A. Corti, R. Dijkgraaf, M. Douglas, J. Gauntlett, M. Gross, C. Hull, A. Jaffe and M. Reid. The early part of the school had many lectures that introduced various concepts of algebraic geometry and string theory with a focus on improving communication between these two fields. During the latter part of the program there were also a number of research level talks. AMS CMI Clay Mathematics Proceedings Volume 3 Strings and Geometry Proceedings of the Clay Mathematics Institute  2002 Summer School Isaac Newton Institute Cambridge, United Kingdom March 24–April 20, 2002 Michael Douglas Jerome Gauntlett Mark Gross Editors American Mathematical Society Clay Mathematics Institute 392 pages • 3/4” spine STRINGS AND GEOMETRY Clay Mathematics Proceedings Volume 3 STRINGS AND GEOMETRY Proceedings of the Clay Mathematics Institute 2002 Summer School on Strings and Geometry Isaac Newton Institute Cambridge, United Kingdom March 24–April 20, 2002 Michael Douglas Jerome Gauntlett Mark Gross Editors American Mathematical Society Clay Mathematics Institute 2000 Mathematics Subject Classification. Primary 81T30, 83E30, 53C29, 32Q25, 14J32, 83E50, 14E15, 53C80, 32S45, 14D20. ISBN 0-8218-3715-X Copying and reprinting. Material in this book may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Clay Mathematics Institute, One Bow Street, Cambridge, MA 02138, USA. Requests can also be made by e-mail to [email protected] Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.) c 2004 by the Clay Mathematics Institute. All rights reserved.
Published by the American Mathematical Society, Providence, RI, for the Clay Mathematics Institute, Cambridge, MA. Printed in the United States of America. The Clay Mathematics Institute retains all rights except those granted to the United States Government. ∞ The paper used in this book is acid-free and falls within the guidelines
established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ Visit the Clay Mathematics Institute home page at http://www.claymath.org/ 10 9 8 7 6 5 4 3 2 1 09 08 07 06 05 04 Contents The Geometry of String Theory Michael