Mathematical Perspectives On Theoretical Physics: A Journey From Black Holes To Superstrings

M A T H E M A T I C A L P E R S P E C T I V E S THEORETICAL ON PHYSICS A Journey from Black Holes to Superstrings M A T H E M A T I C A L P E R S P E C T I V E S THEORETICAL ON PHYSICS A Journey from Black Holes to Superstrings NIRMALA PRAKASH Visting Scientist Massachusetts Institute of Technology, USA /flh Imperial College Press Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202,1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. First published in 2000 by Tata McGraw-Hill Publishing Company Limited Copyright © 2000 by Tata McGraw-Hill Publishing Company Limited MATHEMATICAL PERSPECTIVES ON THEORETICAL PHYSICS A Journey from Black Hole to Superstrings Copyright © 2003 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 1-86094-364-0 ISBN 1-86094-365-0 (pbk) Printed by Fulsland Offset Printing (S) Pte Ltd, Singapore "To the readers of the new millennium PREFACE This text, unlike others, did not grow out of seminar or classroom lectures; instead it grew out of the author's conviction that present day physicists and mathematicians should know the basics of string and superstring theories, just as they know calculus, linear algebra, geometry and analysis. To reach this goal, however, the theory that is pursued at research level in selected schools has to be made available to a wider audience. This is possible only if the teaching (and a text) focuses not only on the string and superstring theories but also provides: (i) the elements of all the prerequisites; (ii) an overview of other great theories that have preceded it (since it uses their phenomenology); and (iii) a motivational thread to reach the end goal. The present text is organized to fulfill these objectives. Since the target here is a much larger population of physicists and mathematicians, we avoid the mathematical rigor. No theorems (with few exceptions) are proved in the main text, in fact they are stated as 'Results' and 'Facts,' and their proofs (in important cases) are given as solutions to the exercises at the end of a section. This offers the reader (the teacher) the option of choosing the preferred level of in-depth/non-depth coverage (in a class). Besides this, the material is often presented using the two points of view (mathematics and physics) which makes the subject easily comprehensible. The first six chapters provide