THE BIRTH OF STRING THEORY - Cambridge University...

THE BIRTH OF STRING THEORY

String theory is currently the best candidate for a unified theory of all forces and all formsof matter in nature. As such, it has become a focal point for physical and philosophical dis-cussions. This unique book explores the history of the theory’s early stages of development,as told by its main protagonists.

The book journeys from the first version of the theory (the so-called Dual ResonanceModel) in the late 1960s, as an attempt to describe the physics of strong interactions outsidethe framework of quantum field theory, to its reinterpretation around the mid-1970s as aquantum theory of gravity unified with the other forces, and its successive developmentsup to the superstring revolution in 1984. Providing important background information tocurrent debates on the theory, this book is essential reading for students and researchers inphysics, as well as for historians and philosophers of science.

andrea cappelli is a Director of Research at the Istituto Nazionale di Fisica Nucleare,Florence. His research in theoretical physics deals with exact solutions of quantum fieldtheory in low dimensions and their application to condensed matter and statistical physics.

elena castellani is an Associate Professor at the Department of Philosophy, Uni-versity of Florence. Her research work has focussed on such issues as symmetry, physicalobjects, reductionism and emergence, structuralism and realism.

filippo colomo is a Researcher at the Istituto Nazionale di Fisica Nucleare, Florence.His research interests lie in integrable models in statistical mechanics and quantum fieldtheory.

paolo di vecchia is a Professor of Theoretical Physics at Nordita, Stockholm, andat the Niels Bohr Institute, Copenhagen. He has worked on several aspects of theoreticalparticle physics, and has contributed to the development of string theory since its birth in1968.

www.cambridge.org© in this web service Cambridge University Press

Cambridge University Press978-0-521-19790-8 - The Birth of String TheoryEdited by Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo Di VecchiaFrontmatterMore information

http://www.cambridge.org/9780521197908http://www.cambridge.orghttp://www.cambridge.org

THE BIRTH OF STRING THEORY

Edited by

ANDREA CAPPELLIINFN, Florence

ELENA CASTELLANIDepartment of Philosophy, University of Florence

FILIPPO COLOMOINFN, Florence

PAOLO DI VECCHIANordita, Stockholm and Niels Bohr Institute, Copenhagen




cambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town,

Singapore, São Paulo, Delhi, Mexico City

Cambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UK

Published in the United States of America by Cambridge University Press, New York

www.cambridge.orgInformation on this title: www.cambridge.org/9780521197908

C© Cambridge University Press 2012

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the written

permission of Cambridge University Press.

First published 2012

Printed in the United Kingdom at the University Press, Cambridge

A catalogue record for this publication is available from the British Library

Library of Congress Cataloguing in Publication dataThe birth of string theory / edited by Andrea Cappelli, INFN, Florence; Elena Castellani,

Department of Philosophy, University of Florence; Filippo Colomo, INFN, Florence;Paolo Di Vecchia, Niels Bohr Institute, Copenhagen and Nordita, Stockholm.

p. cm.Includes bibliographical references and index.

ISBN 978-0-521-19790-81. String models. 2. Duality (Nuclear physics) I. Cappelli, Andrea, editor of compilation.II. Castellani, Elena, 1959– editor of compilation. III. Colomo, F., editor of compilation.

IV. Di Vecchia, P. (Paolo), editor of compilation.QC794.6.S85B57 2012

539.7′258 – dc23 2011052388

ISBN 978-0-521-19790-8 Hardback

Cambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred to

in this publication, and does not guarantee that any content on suchwebsites is, or will remain, accurate or appropriate.




Contents

List of contributors page xPhotographs of contributors xivPreface xxiAbbreviations and acronyms xxiv

Part I Overview 1

1 Introduction and synopsis 3

2 Rise and fall of the hadronic string 17gabriele veneziano

3 Gravity, unification, and the superstring 37john h. schwarz

4 Early string theory as a challenging case study for philosophers 63elena castellani

EARLY STRING THEORY

Part II The prehistory: the analytic S-matrix 81

5 Introduction to Part II 835.1 Introduction 835.2 Perturbative quantum field theory 845.3 The hadron spectrum 885.4 S-matrix theory 915.5 The Veneziano amplitude 97

6 Particle theory in the Sixties: from current algebra to the Venezianoamplitude 100marco ademollo

7 The path to the Veneziano model 116hector r. rubinstein

v




vi Contents

8 Two-component duality and strings 122peter g.o. freund

9 Note on the prehistory of string theory 129murray gell-mann

Part III The Dual Resonance Model 133

10 Introduction to Part III 13510.1 Introduction 13510.2 N -point dual scattering amplitudes 13710.3 Conformal symmetry 14510.4 Operator formalism 14710.5 Physical states 15010.6 The tachyon 153

11 From the S-matrix to string theory 156paolo di vecchia

12 Reminiscence on the birth of string theory 179joel a. shapiro

13 Personal recollections 191daniele amati

14 Early string theory at Fermilab and Rutgers 193louis clavelli

15 Dual amplitudes in higher dimensions: a personal view 198claud lovelace

16 Personal recollections on dual models 202renato musto

17 Remembering the ‘supergroup’ collaboration 208francesco nicodemi

18 The ‘3-Reggeon vertex’ 214stefano sciuto

Part IV The string 219

19 Introduction to Part IV 22119.1 Introduction 22119.2 The vibrating string 22319.3 The rotating rod 22619.4 The relativistic point particle 228




Contents vii

19.5 The string action 23019.6 The quantum theory of the string 231

20 From dual models to relativistic strings 236peter goddard

21 The first string theory: personal recollections 262leonard susskind

22 The string picture of the Veneziano model 266holger b. nielsen

23 From the S-matrix to string theory 275yoichiro nambu

24 The analogue model for string amplitudes 283david b. fairlie

25 Factorization in dual models and functional integration in string theory 294stanley mandelstam

26 The hadronic origins of string theory 312richard c. brower

TOWARDS MODERN STRING THEORY

Part V Beyond the bosonic string 329

27 Introduction to Part V 33127.1 Introduction 33127.2 Chan–Paton factors 33327.3 The Lovelace–Shapiro amplitude 33427.4 The Ramond model 33527.5 The Neveu–Schwarz model 33827.6 The Ramond–Neveu–Schwarz model 33927.7 World-sheet supersymmetry 34127.8 Affine Lie algebras 344

28 From dual fermion to superstring 346david i. olive

29 Dual model with fermions: memoirs of an early string theorist 361pierre ramond

30 Personal recollections 373andré neveu

31 Aspects of fermionic dual models 378edward corrigan




viii Contents

32 The dual quark models 393korkut bardakci and martin b. halpern

33 Remembering the dawn of relativistic strings 407jean-loup gervais

34 Early string theory in Cambridge: personal recollections 414claus montonen

Part VI The superstring 419

35 Introduction to Part VI 42135.1 Introduction 42135.2 The field theory limit 42335.3 Unification of all interactions 42735.4 The QCD string 43135.5 A detour on spinors 43335.6 Spacetime supersymmetry 43435.7 The GSO projection 43735.8 The Kaluza–Klein reduction and supersymmetry breaking 43935.9 The local supersymmetric action for the superstring 44235.10 Supergravity 444

36 Supersymmetry in string theory 447ferdinando gliozzi

37 Gravity from strings: personal reminiscences of early developments 459tamiaki yoneya

38 From the Nambu–Goto to the σ -model action 474lars brink

39 Locally supersymmetric action for the superstring 484paolo di vecchia

40 Personal recollections 490eugène cremmer

41 The scientific contributions of Joël Scherk 496john h. schwarz

Part VII Preparing the string renaissance 509

42 Introduction to Part VII 51142.1 Introduction 51142.2 Supergravity unification of all interactions 51242.3 A novel light-cone formalism 51442.4 Modern covariant quantization 518




Contents ix

42.5 Anomaly cancellation 52142.6 A new era starts or, maybe better, continues 525

43 From strings to superstrings: a personal perspective 527michael b. green

44 Quarks, strings and beyond 544alexander m. polyakov

45 The rise of superstring theory 552andrea cappelli and filippo colomo

Appendix A Theoretical tools of the Sixties 569Appendix B The Veneziano amplitude 579Appendix C From the string action to the Dual Resonance Model 586Appendix D World-sheet and target-space supersymmetry 604Appendix E The field theory limit 620Index 626




Contributors

Marco AdemolloDipartimento di Fisica, Università di Firenze, and INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy

Daniele AmatiSISSA, Trieste, and INFN, Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy

Korkut BardakciDepartment of Physics, University of California, and Theoretical Physics Group,Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720,USA

Lars BrinkDepartment of Fundamental Physics, Chalmers University of Technology,S-412 96 Göteborg, Sweden

Richard C. BrowerPhysics Department, Boston University, 590 Commonwealth Avenue, Boston, MA 02215,USA

Andrea CappelliINFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy

Elena CastellaniDipartimento di Filosofia, Università di Firenze, Via Bolognese 52, 50139 Firenze, Italy

Louis ClavelliDepartment of Physics and Astronomy, University of Alabama, Tuscaloosa, AL35487-0324, USA

x




List of contributors xi

Filippo ColomoINFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy

Edward CorriganDepartment of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK

Eugène CremmerLaboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond,75231 Paris Cedex 05, France

Paolo Di VecchiaNiels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark, and Nordita,Roslagstullsbacken 23, 10691 Stockholm, Sweden

David B. FairlieDepartment of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK

Peter G. O. FreundEnrico Fermi Institute and Department of Physics, University of Chicago,5720 S. Ellis Avenue, Chicago, IL 60637, USA

Murray Gell-MannSanta Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

Jean-Loup GervaisLaboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond,75231 Paris Cedex 05, France

Ferdinando GliozziDipartimento di Fisica Teorica, Università di Torino, and INFN, Sezione di Torino,Via P. Giuria 1, 10125 Torino, Italy

Peter GoddardInstitute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA

Michael B. GreenDAMTP, Wilberforce Road, Cambridge, CB3 0WD, UK

Martin B. HalpernDepartment of Physics, University of California, and Theoretical Physics Group,Lawrence Berkeley National Laboratory, University of California, Berkeley, CA94720, USA




xii List of contributors

Claud LovelaceDepartment of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road,Piscataway, NJ 08854-8019, USA

Stanley MandelstamDepartment of Physics, University of California, and Lawrence Berkeley Laboratory,University of California, Berkeley, CA 94720, USA

Claus MontonenDepartment of Physics, University of Helsinki, P.O. Box 64, 00014 Helsinki, Finland

Renato MustoDipartimento di Scienze Fisiche, Università di Napoli Federico II, and INFN,Sezione di Napoli, 80126, Napoli, Italy

Yoichiro NambuDepartment of Physics, University of Chicago, 5720 S. Ellis Avenue, Chicago, IL 60637,USA

André NeveuLaboratoire de Physique Théorique et Astroparticules, Case 070, CNRS,Université Montpellier II, 34095 Montpellier, France

Francesco NicodemiDipartimento di Scienze Fisiche, Università di Napoli Federico II, and INFN,Sezione di Napoli, 80126, Napoli, Italy

Holger B. NielsenNiels Bohr Institute, Blegdamsvej 17, 2100, Copenhagen, Denmark

David I. OliveDepartment of Physics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK

Alexander M. PolyakovJoseph Henry Laboratories, Princeton University, Princeton, NJ 08544, USA

Pierre RamondInstitute for Fundamental Theory, Physics Department, University of Florida, Gainesville,FL 32611, USA

Hector R. RubinsteinAlbaNova University Center, Royal Institute of Technology, Stockholm University,106 91 Stockholm, Sweden




List of contributors xiii

John H. SchwarzDepartment of Physics, Mathematics and Astronomy, California Institute of Technology,456 Lauritsen Laboratory Caltech 452-48, Pasadena, CA 91125, USA

Stefano SciutoDipartimento di Fisica Teorica, Università di Torino, and INFN, Sezione di Torino,Via P. Giuria 1, 10125 Torino, Italy

Joel A. ShapiroDepartment of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road,Piscataway, NJ 08854-8019, USA

Leonard SusskindDepartment of Physics, Stanford University, Stanford, CA 94305-4060, USA

Gabriele VenezianoTheory Division, CERN, CH-1211 Geneva 23, Switzerland, and Collège de France,11 place M. Berthelot, 75005 Paris, France

Tamiaki YoneyaInstitute of Physics, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan




Photographs of contributors

From left to right and from top to bottom: Marco Ademollo, Daniele Amati, Korkut Bardakci, LarsBrink, Richard C. Brower and Louis Clavelli.

xiv




Photographs of contributors xv

From left to right and from top to bottom: Edward Corrigan, Eugène Cremmer, Paolo Di Vecchia,David B. Fairlie, Peter G. O. Freund, Sergio Fubini (1928–2005), Murray Gell-Mann, Jean-LoupGervais and Ferdinando Gliozzi.




xvi Photographs of contributors

From left to right and from top to bottom: Peter Goddard, Michael B. Green, Martin B. Halpern,Claud Lovelace, Stanley Mandelstam, Claus Montonen, Renato Musto, Yoichiro Nambu and AndréNeveu [photograph of Goddard by Cliff Moore].




Photographs of contributors xvii

From left to right and from top to bottom: Francesco Nicodemi, Holger B. Nielsen, David I. Olive,Alexander M. Polyakov, Pierre Ramond, Hector R. Rubinstein (1933–2009), Bunji Sakita (1930–2002), Joël Scherk (1946–1980) and John H. Schwarz.




xviii Photographs of contributors

From left to right and from top to bottom: Stefano Sciuto, Joel A. Shapiro, Leonard Susskind, GabrieleVeneziano and Tamiaki Yoneya.




Part

icip

ants

atth

em

eetin

g‘T

heB

irth

ofSt

ring

The

ory’

,18–

19M

ay20

07,G

GI,

Arc

etri

,Flo

renc

e.




Preface

In May 2007 we organized a workshop on the origin and early developments of string theoryat the Galileo Galilei Institute for Theoretical Physics in Arcetri (Florence). A fair numberof researchers who had contributed to the birth of the theory participated and described,according to their personal recollections, the intriguing way in which the theory developedfrom hadron phenomenology into an independent field of research. It was the first occasionon which they had all been brought together since the 1975 conference in Durham, whichrepresented the last meeting on string theory as applied to hadronic physics.

The workshop in Arcetri was a success: the atmosphere was enthusiastic and the par-ticipants showed genuine pleasure in discussing the lines of thought developed during theyears from the late Sixties to the beginning of the Eighties, mutually checking their ownreminiscences. This encouraged us to go on with the project we had been thinking of forsome time, of an historical account of the early stages of string theory based on the recol-lections of its main exponents. We were fortunate enough to have on board practically allthe physicists who developed the theory. While some of the contributions to this Volumeoriginated from the talks presented at the meeting, most of them have been written expresslyfor this book.

In starting this project we were motivated by the observation that the history of thebeginnings and early phases of string theory is not well accounted for: apart from theoriginal papers, the available literature is rather limited and fragmentary. A book devotedspecifically to the historical reconstruction of these developments – the formulation of aconsistent and beautiful theory starting from hadron phenomenology, its failure as a theoryof strong interactions, and, finally, its renaissance as a unified theory of all fundamentalinteractions – was not available. This Volume aims to fill the gap, by offering a collection ofreminiscences and overviews, each one contributing from the Author’s own perspective tothe general historical account. The collection is complemented with an extended editorialapparatus (Introductions, Appendices and Editors’ Chapters) according to criteria explainedbelow.

In addition to the historical record, this book is of interest for several reasons. First,by showing the dynamics of the ideas, concepts and methods involved, it offers preciousbackground information for a better understanding of the present status of string theory,

xxi




xxii Preface

which has recently been at the centre of a widespread debate. Second, it provides an illus-tration of the fruitfulness of the field, from both a physical and a mathematical perspective.A number of ideas that are central to contemporary theoretical physics of fundamentalinteractions, such as supersymmetry and extra spacetime dimensions, originated in thiscontext. Furthermore, some theoretical methods, for example two-dimensional conformalsymmetry, found important physical applications in various domains outside the originalone. Finally, from a philosophical point of view, early string theory represents a particularlyinteresting case study for reflections on the construction and evaluation of physical theoriesin modern physics.

In the following, we illustrate the structure of the book and offer some guidelines to thereader. The Volume is organized into seven Parts: the first one provides an overview of thewhole book; the others correspond to significant stages in the evolution of string theoryfrom 1968 to 1984 and are accompanied by specific introductory Chapters.

In Part I, the Introduction summarizes the main developments and contains a tempo-ral synopsis with a list of key results and publications. The following two Chapters, byVeneziano and by Schwarz, offer a rather broad overview on the early (1968–1973) andlater (1974–1984) periods of the history of string theory, respectively. They introduce allthe themes of the book that are then addressed in detail in the following Parts. The lastChapter of Part I, by Castellani, presents some elements for the philosophical discussionof the early evolution of the theory and the scientific methodology employed in it.

The Introductions to the other Parts and the Appendices are meant to fit the needs ofundergraduate/early graduate students in theoretical physics, as well as of historians andphilosophers, who have a background in quantum mechanics and quantum field theory, butlack the specific vocabulary to appreciate fully the Authors’ contributions. The Introductionsand Appendices, taken together with the final Chapter, can also be used as an entry-levelcourse in string theory, presenting the main physical ideas with a minimum of technique.

For a broader audience, we suggest beginning with the first, nontechnical paragraphin each Introduction, and then approaching the less technical and more comprehensiveAuthors’ Chapters which are located first in each Part. The rich material presented inthe Chapters, together with the original literature, can be the starting point for in-depthhistorical study of the many events that took place in the development of string theory.The final Chapter of the book, by Cappelli and Colomo, provides a nontechnical overviewof string theory from 1984 up to the present time, which complements the historical andscientific perspective.

We hope that the book can be read at different levels and, as such, will be useful forscientific, historical and philosophical approaches to this fascinating, but complex, subject.

The book has associated the webpage

http://theory.fi.infn.it/colomo/string-book/

which gives access to the original talks of the 2007 GGI workshop and to additional materialalready provided by some Authors or to be collected in the future.




Preface xxiii

We are very grateful to all those who have helped us in preparing this Volume. First andforemost, our thanks go to all the Authors who agreed to contribute their reminiscences.Many thanks go also to all those who gave us valuable comments and suggestions duringthe preparation of the Volume, in particular Leonardo Castellani, Camillo Imbimbo, YuriMakeenko, Raffaele Marotta, Giulio Peruzzi, Igor Pesando, Franco Pezzella, AugustoSagnotti, John H. Schwarz, Domenico Seminara, Gabriele Veneziano, Guillermo R. Zembaand Hans v. Zur-Mühlen. We are indebted to the Galileo Galilei Institute for hosting the 2007workshop. We also wish to thank the staff of Cambridge University Press for assistanceand Sara De Sanctis for helping with the bibliography. Finally, we are grateful to ourcollaborators and to our families for their patience and support.




Abbreviations and acronyms

AdS Anti de Sitter (spacetime)AdS/CFT Anti de Sitter/conformal field theory (correspondence)APS American Physical SocietyBRST Becchi–Rouet–Stora–Tyutin (quantization)Caltech California Institute of Technology, Pasadena, CACERN European Centre for Nuclear Research, GenevaCFT conformal field theoryCNRS Centre National de la Recherche Scientifique, FranceCP Chan–Paton (factors)CPT charge conjugation, parity, time reversal (symmetries)DAMTP Department of Applied Mathematics and Theoretical Physics, CambridgeDDF Del Giudice–Di Vecchia–Fubini (states, operators)DHS Dolen–Horn–Schmid (duality)Dp-brane Dirichlet p-dimensional membraneDRM Dual Resonance ModelENS École Normale Supérieure, ParisFermilab Fermi National Accelerator Laboratory (or FNAL), IllinoisFESR finite energy sum ruleFNAL Fermi National Accelerator Laboratory (or Fermilab), IllinoisGGI Galileo Galilei Institute, FlorenceGGRT Goddard–Goldstone–Rebbi–Thorn (quantization)GR general relativityGSO Gliozzi–Scherk–Olive (projection)GUT Grand Unified TheoriesIAS Institute of Advanced Study, Princeton, NJICTP International Center for Theoretical Physics, TriesteIHES Institut des Hautes Études Scientifiques, Bures-sur-YvetteIMF infinite momentum frameINFN Istituto Nazionale di Fisica Nucleare, ItalyIR infraredISR Intersecting Storage Ring, CERN

xxiv




Abbreviations and acronyms xxv

ITP (Kavli) Institute of Theoretical Physics, Santa Barbara, CAKK Kaluza–Klein (compactification)KM Kac–Moody (algebra)KN Koba–Nielsen (amplitudes)KZ Knizhnik–Zamolodchikov (equation)LEP Large Electron–Positron (collider), CERNLHC Large Hadron Collider, CERNLPTENS Laboratoire de Physique Théorique, École Normale Supérieure, ParisLPTHE Laboratoire de Physique Théorique et Hautes Energies, OrsayMIT Massachusetts Institute of Technology, Boston, MAMSSM Minimal Supersymmetric Standard ModelM-theory matrix (or membrane) theoryNAL National Accelerator Laboratory (FNAL after 1972), IllinoisNATO North Atlantic Treaty OrganizationNordita Nordic Institute for Theoretical Physics, StockholmNS Neveu–Schwarz (model, sector)NSF National Science Foundation, USANYU New York UniversityPCAC partially conserved axial currentPS Proton Synchrotron, CERNQCD quantum chromodynamicsQED quantum electrodynamicsQFT quantum field theoryR Ramond (model, sector)RIMS Research Institute for Mathematical Sciences, KyotoRNS Ramond–Neveu–Schwarz (model)SISSA Scuola Internazionale Superiore di Studi Avanzati, TriesteSLAC Stanford Linear Accelerator CenterS-matrix scattering matrixSM Standard ModelSSC Superconducting Super ColliderSSR superconvergence sum ruleSUGRA supergravitySUSY supersymmetrySVM Shapiro–Virasoro modelTOE Theory of EverythingUV ultravioletWZ Wess–Zumino (model)WZWN Wess–Zumino–Witten–Novikov (model)YM Yang–Mills (gauge theory)




http://www: cambridge: org:

9780521197908:

THE BIRTH OF STRING THEORY - Cambridge University...

Documents

Transcript of THE BIRTH OF STRING THEORY - Cambridge University...