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The Birth of String Theory THE BIRTH OF STRING THEORY String theory is currently the best candidate for a unified theory of all forces and all forms of 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 Resonance Model) in the late 1960s, as an attempt to describe the physics of strong interactions outside the framework of quantum field theory, to its reinterpretation around the mid-1970s as a quantum theory of gravity unified with the other forces, and its successive developments up to the superstring revolution in 1984. Providing important background information to current debates on the theory, this book is essential reading for students and researchers in physics, 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 field theory 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, physical objects, 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 field theory. paolo di vecchia is a Professor of Theoretical Physics at Nordita, Stockholm, and at the Niels Bohr Institute, Copenhagen. He has worked on several aspects of theoretical particle physics, and has contributed to the development of string theory since its birth in 1968. THE 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 Nordita, Stockholm and Niels Bohr Institute, Copenhagen cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao˜ Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521197908 C Cambridge University Press 2012 This publication is in copyright. Subject to statutory exception and 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 data The 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 978-0-521-19790-8 1. 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 539.7258 – dc23 2011052388 ISBN 978-0-521-19790-8 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents List of contributors page x Photographs of contributors xiv Preface xxi Abbreviations and acronyms xxiv Part I Overview 1 1 Introduction and synopsis 3 2 Rise and fall of the hadronic string 17 gabriele veneziano 3 Gravity, unification, and the superstring 37 john h. schwarz 4 Early string theory as a challenging case study for philosophers 63 elena castellani EARLY STRING THEORY Part II The prehistory: the analytic S-matrix 81 5 Introduction to Part II 83 5.1 Introduction 83 5.2 Perturbative quantum field theory 84 5.3 The hadron spectrum 88 5.4 S-matrix theory 91 5.5 The Veneziano amplitude 97 6 Particle theory in the Sixties: from current algebra to the Veneziano amplitude 100 marco ademollo 7 The path to the Veneziano model 116 hector r. rubinstein v vi Contents 8 Two-component duality and strings 122 peter g.o. freund 9 Note on the prehistory of string theory 129 murray gell-mann Part III The Dual Resonance Model 133 10 Introduction to Part III 135 10.1 Introduction 135 10.2 N-point dual scattering amplitudes 137 10.3 Conformal symmetry 145 10.4 Operator formalism 147 10.5 Physical states 150 10.6 The tachyon 153 11 From the S-matrix to string theory 156 paolo di vecchia 12 Reminiscence on the birth of string theory 179 joel a. shapiro 13 Personal recollections 191 daniele amati 14 Early string theory at Fermilab and Rutgers 193 louis clavelli 15 Dual amplitudes in higher dimensions: a personal view 198 claud lovelace 16 Personal recollections on dual models 202 renato musto 17 Remembering the ‘supergroup’ collaboration 208 francesco nicodemi 18 The ‘3-Reggeon vertex’ 214 stefano sciuto Part IV The string 219 19 Introduction to Part IV 221 19.1 Introduction 221 19.2 The vibrating string 223 19.3 The rotating rod 226 19.4 The relativistic point particle 228 Contents vii 19.5 The string action 230 19.6 The quantum theory of the string 231 20 From dual models to relativistic strings 236 peter goddard 21 The first string theory: personal recollections 262 leonard susskind 22 The string picture of the Veneziano model 266 holger b. nielsen 23 From the S-matrix to string theory 275 yoichiro nambu 24 The analogue model for string amplitudes 283 david b. fairlie 25 Factorization in dual models and functional integration in string theory 294 stanley mandelstam 26 The hadronic origins of string theory 312 richard c. brower TOWARDS MODERN STRING THEORY Part V Beyond the bosonic string 329 27 Introduction to Part V 331 27.1 Introduction 331 27.2 Chan–Paton factors 333 27.3 The Lovelace–Shapiro amplitude 334 27.4 The Ramond model 335 27.5 The Neveu–Schwarz model 338 27.6 The Ramond–Neveu–Schwarz model 339 27.7 World-sheet supersymmetry 341 27.8 Affine Lie algebras 344 28 From dual fermion to superstring 346 david i. olive 29 Dual model with fermions: memoirs of an early string theorist 361 pierre ramond 30 Personal recollections 373 andre´ neveu 31 Aspects of fermionic dual models 378 edward corrigan viii Contents 32 The dual quark models 393 korkut bardakci and martin b. halpern 33 Remembering the dawn of relativistic strings 407 jean-loup gervais 34 Early string theory in Cambridge: personal recollections 414 claus montonen Part VI The superstring 419 35 Introduction to Part VI 421 35.1 Introduction 421 35.2 The field theory limit 423 35.3 Unification of all interactions 427 35.4 The QCD string 431 35.5 A detour on spinors 433 35.6 Spacetime supersymmetry 434 35.7 The GSO projection 437 35.8 The Kaluza–Klein reduction and supersymmetry breaking 439 35.9 The local supersymmetric action for the superstring 442 35.10 Supergravity 444 36 Supersymmetry in string theory 447 ferdinando gliozzi 37 Gravity from strings: personal reminiscences of early developments 459 tamiaki yoneya 38 From the Nambu–Goto to the σ-model action 474 lars brink 39 Locally supersymmetric action for the superstring 484 paolo di vecchia 40 Personal recollections 490 eugene` cremmer 41 The scientific contributions of Joel¨ Scherk 496 john h. schwarz Part VII Preparing the string renaissance 509 42 Introduction to Part VII 511 42.1 Introduction 511 42.2 Supergravity unification of all interactions 512 42.3 A novel light-cone formalism 514 42.4 Modern covariant quantization 518 Contents ix 42.5 Anomaly cancellation 521 42.6 A new era starts or, maybe better, continues 525 43 From strings to superstrings: a personal perspective 527 michael b. green 44 Quarks, strings and beyond 544 alexander m. polyakov 45 The rise of superstring theory 552 andrea cappelli and filippo colomo Appendix A Theoretical tools of the Sixties 569 Appendix B The Veneziano amplitude 579 Appendix C From the string action to the Dual Resonance Model 586 Appendix D World-sheet and target-space supersymmetry 604 Appendix E The field theory limit 620 Index 626 Contributors Marco Ademollo Dipartimento di Fisica, Universita` di Firenze, and INFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy Daniele Amati SISSA, Trieste, and INFN, Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy Korkut Bardakci Department of Physics, University of California, and Theoretical Physics Group, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA Lars Brink Department of Fundamental Physics, Chalmers University of Technology, S-412 96 Goteborg,¨ Sweden Richard C. Brower Physics Department, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA Andrea Cappelli INFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy Elena Castellani Dipartimento di Filosofia, Universita` di Firenze, Via Bolognese 52, 50139 Firenze, Italy Louis Clavelli Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487-0324, USA x List of contributors xi Filippo Colomo INFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy Edward Corrigan Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK Eugene` Cremmer Laboratoire de Physique Theorique,´ Ecole´ Normale Superieure,´ 24 rue Lhomond, 75231 Paris Cedex 05, France Paolo Di Vecchia Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark, and Nordita, Roslagstullsbacken 23, 10691 Stockholm, Sweden David B.
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