SUPERSTRINGS, UNIFIED THEORIES AND COSMOLOGY This page is intentionally left blank THE ICTP SERIES IN THEORETICAL PHYSICS - VOLUME 3 SUPERSTRINGS, UNIFIED THEORIES AND COSMOLOGY Proceedings of the Summer Workshop in High Energy Physics and Cosmology Trieste, Italy 30 June - 15 August 1986 editors G FURLAN R JENGO J C PATI DWSCIAMA E SEZGIN QSHAFI 9 World Scientific Published by World Scientific Publishing Co. Pte. Ltd. P. 0. Box 128, Farrer Road, Singapore 9128 Library of Congress Cataloging-in-Publication data is available. SUPERSTRINGS, UNIFIED THEORIES AND COSMOLOGY Copyright© 1987 by World Scientific Publishing Co Pte Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photo copying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. ISBN 9971-50-271-2 Printed in Singapore by Kim Hup Lee Printing Co. Pte. Ltd. v PREFACE The International Centre for Theoretical Physics in Trieste has been running a Summer Workshop in High Energy Physics and Cosmology since 1981. The primary goal of these workshops is to bring together active physicists from around the world -particularly from developing countries -and to provide a platform where the frontier developments in the field are presented by leading workers and pioneers over a period of four to five weeks. The 1986 workshop was very active and we believe stimulating. There, were over one hundred participants from many different countries. There were extensive lectures and discussions on many topics including string theories, two-dimensional conformal invariant field theories, compactification schemes, supersymmetry, supergravity, preonic theories, and cosmology. As in the previous years, we were fortunate that all the areas mentioned above were presented by leading physicists in the fields. We gratefully acknowledge the participation of all the lecturers. We particularly thank those who took the trouble in making their lecture notes available for publication in the proceedings. The workshop has benefited immensely from the constant inspiration provided by Professor Abdus Salam. The constant help of the ICTP staff was essential for the smooth running of the workshop. G. Furlan R. Jengo J. C. Pati D. W. Sciama E. Sezgin 0. Shafi This page is intentionally left blank vii CONTENTS Preface v The Spinning String P. Di Vecchia Riemann Surfaces and String Theory 21 E. Gava The Bosonic String from an Algebro-geometric Standpoint 38 M. Cornalba Classical and Quantum Theory of Supersymmetric a-Models 53 S. Mukhi Non-linear a-Models and String Theories 71 A. Sen Virasoro Gauge Conditions and String Equations of Motion 100 S. R. Wadia Antisymmetric Tensor Fields in String Theory 114 R. Rohm Toroidal Compactification of Heterotic String 132 K. S. Narain (p, 0) Supergravity and H~terotic Superstrings 133 M. Evans and B. A. Ovrut Topics in Superstring Theory 167 P. H. Frampton viii Field Theory of Strings 176 K. Kikkawa Introduction to Covariant Formulation of Superstring (Field) Theory 222 S. Uehara Towards a Superstring Cosmology 238 J. G. Taylor The Interacting Field Theories of Strings and Superstrings 248 M.A. Awada Manifold Compactification of Superstrings 274 T. Hiibsch New Issues in Supergravity Theories 295 L. Girardello Some Questions Concerning the Low-energy Limit of Superstring Theories 318 H. P. Nilles Superstrings and Preons : New Dynamics and a New Approach to Unification 332 J. C. Pati Neutrino Mass, Flavor and Mixing in Cosmology 363 R. Cowsik Dynamics of Galaxies Embedded in Dark Matter 375 R. Cowsik Physics of the Early Universe : The Inflationary Universe and Cosmic Strings 388 R. H. Brandenberger Dynamically Generated Fermionic Masses 443 M. Cvetic SUPERSTRINGS, UNIFIED THEORIES AND COSMOLOGY