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The Quantum Structure of Space and Time QcEntwn Structure &pace and Time This page intentionally left blank Proceedings of the 23rd Solvay Conference on Physics Brussels, Belgium 1 - 3 December 2005 The Quantum Structure of Space and Time EDITORS DAVID GROSS Kavli Institute. University of California. Santa Barbara. USA MARC HENNEAUX Universite Libre de Bruxelles & International Solvay Institutes. Belgium ALEXANDER SEVRIN Vrije Universiteit Brussel & International Solvay Institutes. Belgium \b World Scientific NEW JERSEY LONOON * SINGAPORE BElJlNG * SHANGHAI HONG KONG TAIPEI * CHENNAI Published by World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore 596224 USA ofJice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK ofice; 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-PublicationData A catalogue record for this hook is available from the British Library. THE QUANTUM STRUCTURE OF SPACE AND TIME Proceedings of the 23rd Solvay Conference on Physics Copyright 0 2007 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereoi 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 981-256-952-9 ISBN 981-256-953-7 (phk) Printed in Singapore by World Scientific Printers (S) Pte Ltd The International Solvay Institutes Board of Directors Members Mr. Jacques Solvay President Prof. Franz Bingen Vice-president and Emeritus-Professor at the VUB Baron Daniel Janssen President of the Board of Directors of Solvay S.A. Prof. Franklin Lambert Deputy Director and Professor at the VUB Prof. Renk Lefever Professor at the ULB Prof. Grkgoire Nicolis Professor at the ULB Mr Jean-Marie Piret Attorney General of the Supreme Court of Appeal and Honorary Principal Private Secretary to the King Prof. Jean-Louis Vanherweghem President of the Administrative Board of the ULB Prof. Irina Veretennicoff Professor at the VUB Honorary Member Baron Andre Jaumotte Honorary Rector and Honorary President of the ULB Vi The Quantum Structure of Space and Time Guest Members Prof. Albert Goldbeter Professor at the ULB and Scientific Secretary of the Committee for Chemistry Mr Pascal De Wit Adviser Solvay S.A. Prof. Niceas Schamp Secretary of the Royal Flemish Academy for Science and the Arts Prof. Alexandre Sevrin Professor at the VUB and Scientific Secretary of the Committee for Physics Direct or Prof. Marc Henneaux Professor at the ULB The International Solvay Institutes vii Solvay Scientific Committee for Physics Professor Herbert Walther (chair) Max-Planck Institut (Munich, Germany) Professor Tito Arecchi Universith di Firenze and INOA (Firenze, Italy) Professor Jocelyn Bell Burnell University of Bath (Bath, UK) Professor Claude Cohen-Tannoudji Ecole Normale SupBrieure (Paris, fiance) Professor Ludwig Faddeev V.A Steklov Mathematical Institute (Saint-Petersburg, Russia) Professor David Gross Kavli Institute (Santa Barbara, USA) Professor Gerard 't Hooft Spinoza Instituut (Utrecht, The Netherlands) Professor Klaus von Klitzing Max-Planck-Institut (Stuttgart, Germany) Professor Pierre Ramond University of Florida (Gainesville, USA) Professor Alexandre Sevrin (Scientific Secretary) Vrije Universiteit Brussel (Belgium) This page intentionally left blank 23rd Solvay Conference on Physics Hotel MQtropole (Brussels), 1-3 December 2005 The Quantum Structure of Space and Time Chair: Professor David Gross The 23rd Solvay Conference on Physics took place in Brussels from December 1 through December 3, 2005 according to the tradition initiated by Lorentz at the 1st Solvay Conference on Physics in 1911 (“Premier Conseil de Physique Solvay”). It was followed on December 4 by a public event co-organized with the European Commission, during which R. Dijkgraaf and B. Greene delivered public lectures and a panel of scientists (T. Damour, R. Dijkgraaf, B. Greene, D. Gross, G. ’t Hooft, L. Randall, G. Veneziano) answered questions from the audience. The Solvay Conferences have always benefitted from the support and encourage- ment of the Royal Family. His Royal Highness Prince Philippe of Belgium attended the first session on December 1 and met some of the participants. The organization of the 23rd Solvay Conference has been made possible thanks to the generous support of the Solvay Family, the Solvay Company, the Belgian National Lottery, the “Universitb Libre de Bruxelles”, the “Vrije Universeit Brus- sel”, the “Communautk franCaise de Belgique”, the David and Alice Van Buuren Foundation and the H6tel Mbtropole. ix X The Quantum Structure of Space and Tame Participants Nima Arkani-Hamed Harvard Abhay Ashtekar Penn State Michael Atiyah Edinburgh Constantin Bachas Paris Tom Banks Rutgers Lars Brink Goteborg Robert Brout Brussels Claudio Bunster Valdivia Curtis Callan Princeton Thi bault Damour Bures-sur-Yvette Jan de Boer Amsterdam Bernard de Wit Utrecht Robbert Dijkgraaf Amsterdam Michael Douglas Rutgers Georgi Dvali New York Franqois Englert Brussels Ludwig Faddeev St-Petersburg Pierre Fayet Paris Willy Fischler Austin Peter Galison Harvard Murray Gell-Mann Santa Fe Gary Gibbons Cambridge (UK) Michael Green Cambridge (UK) Brian Greene Columbia David Gross Santa Barbara Alan Guth Cambridge (USA) Jeffrey Harvey Chicago Gary Horowitz Santa Barbara Bernard Julia Paris Shamit Kachru Stanford Renata Kallosh St anford Elias Kiritsis Palaiseau Igor Klebanov Princeton Andrei Linde St anford Dieter Lust Munich Juan Maldacena Princeton Nikita Nekrasov Bures-sur-Yvette Hermann Nicolai Potsdam Hirosi Ooguri Pasadena Joseph Polchinski Santa Barbara Alexander Polyakov Princeton Eliezer Rabinovici Jerusalem Pierre Ramond Gainesville Lisa Randall Harvard Valery Rubakov Moscow John S chwarz Pasadena Nathan Seiberg Princeton 23rd Solvay Conference on Physics xi Ashoke Sen Allahabad Stephen Shenker Stanford Eva Silverstein Stanford Paul Steinhardt Princeton Andrew Strominger Harvard Gerard ’t Hooft Utrecht Neil Turok Cambridge Gabriele Veneziano Paris Steven Weinberg Austin Frank Wilczek Cambridge(US A) Paul Windey Paris Shing-Tung Yau H arvar d xii The Quantum Structure of Space and Time Auditors Riccardo Argurio ULB Glenn Barnich ULB Ben Craps VUB Frank Ferr ar i ULB Jean-Marie Fr&e ULB Raymond Gast mans KUL Marc Henneaux ULB Thomas Hertog CERN Laurent Houart ULB Franklin Lambert VUB Christiane Schomblond ULB Alexander Sevrin VUB Philippe Spindel UMH Peter Tinyakov ULB Walter Troost KUL Jan Troost ENS Michel Tytgat ULB Antoine Van Proeyen KUL Opening Session Opening Address by Marc Henneaux Your Royal Highness, Mrs. and Mr. Solvay, Ladies and Gentlemen, Dear Colleagues, Dear Friends, About one hundred years ago, at the invitation of Ernest Solvay, the leading physicists of the time gathered in the hotel Mktropole for a 6-day mythical meeting. This meeting began a tradition of unique conferences that shaped modern science. A total of 22 conferences have taken place every three years except during war periods, covering most aspects at the frontiers of physics. This year’s meeting continues the tradition. It is a great honor for me and a moving moment to welcome all of you to the 23rd Solvay Conference in Physics, in the building where the first meeting took place. A distinctive feature of the Solvay Conferences is that they benefit from the support and encouragement of the Royal Family. The pictures of Einstein with the Queen Elisabeth of Belgium are in the mind of all physicists. It is with a respectful gratitude that we acknowledge the continuation of this tradition today, at the time of the celebration of the 175th anniversary of Belgium. At the start of the 23rd Solvay Conference, I would like to have a thought for Ernest Solvay, the Founder of the Institutes, and for the men who assisted him in this enterprise, Paul Hkger and Hendrik Lorentz. Born in 1838, Ernest Solvay exhibited a passion for physics and chemistry from a very young age. He developed a new process for industrial production of sodium carbonate (NazCOs - “soude” in French, not soda^" (in the plural) as I could see on some uncontrolled web side). This was at the origin of his wealth, which he used to create many charitable foundations. In particular, after the success of the 1911 Solvay Conference, he founded the International Institute of Physics. The mission of the Institute was “to promote research, the purpose of which is to enlarge and deepen our understanding of natural phenomena, without excluding problems ... Xlll xiv The Quantum Structure of Space and Time belonging to other areas of science provided that these are connected with physics”. Mr. Solvay, we are very fortunate that the same interest in fundamental science has been transmitted to the following generations. Paul HBger and Hkndrik Lorentz played also a central role in the foundation of the Institutes. H6ger was professor at the UniversitB Libre de Bruxelles and a close collaborator of Ernest Solvay. He wrote in 1912 the rules of the Institute of Physics with the Dutch theoretical physicist Hendrik Lorentz, 1902 Nobel Laureate. Lorentz was the first scientific chair of the Institute until his death in 1928. He “governed” (if I can say so) the Institute with an iron hand in a velvet glove. His exceptional
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