Lecture Notes in Physics

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Christian Caron Springer Heidelberg Physics Editorial Department I Tiergartenstrasse 17 69121 Heidelberg / Germany [email protected] M. Gasperini J. Maharana (Eds.)

String Theory and Fundamental Interactions

Gabriele Veneziano and Theoretical Physics: Historical and Contemporary Perspectives

13 Editors Maurizio Gasperini Jnan Maharana Universita` di Bari Institute of Physics Dipartimento di Fisica Sachivalaya Marg Via G. Amendola,173 Bhubaneswar - 751 005 70126 Bari, Italy Orissa, India [email protected] [email protected]

M. Gasperini and J. Maharana (Eds.), String Theory and Fundamental Interactions, Lect. Notes Phys. 737 (Springer, Berlin Heidelberg 2008), DOI 10.1007/ 978-3-540-74233-3

Library of Congress Control Number: 2007934340

ISSN 0075-8450 ISBN 978-3-540-74232-6 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2008 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Typesetting: by the authors and Integra using a Springer LATEX macro package Cover design: eStudio Calamar S.L., F. Steinen-Broo, Pau/Girona, Spain Printed on acid-free paper SPIN: 12070305 5 4 3 2 1 0 To Gabriele from his friends, with best wishes Preface

This book has been prepared to celebrate the 65th birthday of Gabriele Veneziano and his retirement from CERN in September 2007. This retire- ment certainly will not mark the end of his extraordinary scientific career (in particular, he will remain on the permanent staff of the Coll`ege de France in Paris), but we believe that this important step deserves a special celebration, and an appropriate recognition of his monumental contribution to physics. Our initial idea of preparing a volume of Selected papers of Professor Gabriele Veneziano, possibly with some added commentary, was dismissed when we realized that this format of book, very popular in former times, has become redundant today because of the full “digitalization” of all important physical journals, and their availability online in the electronic archives. We have thus preferred an alternative (and unconventional, but probably more effective) form of celebrating Gabriele’s birthday: a collection of new papers written by his main collaborators and friends on the various aspects of theo- retical physics that have been the object of his research work, during his long and fruitful career. Selecting a reasonable number of invited contributors and contributed top- ics has proved to be a very difficult task, given the impressive number of dis- tinguished collaborators (see the full list in the first chapter of this book), and the exceptionally wide spectrum of research interests. After a careful analysis of four decades of work, we have finally decided to invite only a few repre- sentative contributions, trying to provide a survey of most of the many faces of Gabriele’s activity, and to avoid, at the same time, too many overlaps and too large gaps. We have been assisted in this process by Gabriele himself, but we are responsible for any important omission, of course. We hope, however, that the reader will appreciate the time (and space) limitations of this book, since making a complete and detailed survey of all of Gabriele’s activities is surely impossible. The contributors have been invited to prepare high-level (but not too much specialized) lectures on the assigned themes, with some introductory part and, possibly, some historical perspective concerning their work with Gabriele. VIII Preface

We are very grateful to our colleagues and friends for having accepted our invitation, and for their excellent scientific and pedagogic work: Daniele Amati Adi Armoni Ram Brustein Alessandra Buonanno Marcello Ciafaloni Thibault Damour Paolo Di Vecchia Sergio Ferrara Alberto Giovannini Massimo Giovannini Kenichi Konishi Giuseppe Marchesini Krzysztof Meissner Roberto Petronzio Eliezer Rabinovici Giancarlo Rossi Hector Rubinstein Adam Schwimmer Mikhail Shifman Graham Shore Tomasz Taylor Luca Trentadue Henry Tye Carlo Ungarelli Gregory Vilkovisky Miguel Virasoro Should this book have any form of success and appreciation, the merit will rest on their dedicated and enthusiastic work, and on the many hours of their valuable time spent on the materialization of this project. We would also like to thank Christian Caron, Senior Editor of Physics at Springer, for his kind encouragement, advice, and for many important suggestions. This book is divided into various parts. The introductory part is fully de- voted to Gabriele Veneziano, and contains a short biography summarizing his main successes and achievements (to date), a full updated list of his collabo- rators and of his publications, and a short interview concerning his personal point of view about the present and future of fundamental physics. We have also included the Latex version of an old, unpublished (and handwritten) note, dating back to 1973, that Gabriele discovered after a long search in his office at CERN. Apart from the genuine historical value of such a document (see, for instance, the comments added by the author for the edition of this book), parts of the original draft are still of interest, and potentially relevant for modern applications. Preface IX

The rest of the book is divided into the following seven parts:

Part 1 – Dual resonance models and string theory Part 2 – Perturbative QCD Part 3 – Non-perturbative QCD Part 4 – Supersymmetric gauge theories Part 5 – String dualities and symmetries Part 6 – String/quantum gravity, black holes, and entropy Part 7 – String cosmology

Each of these parts contains from a minimum of two to a maximum of five articles (organized in historical or pedagogical order), illustrating different aspects of these fields with special emphasis on the contribution of Gabriele and of his collaborators. The result is a rather unconventional, “unique” book where old and new scientific results are mixed with personal memories and feelings of the authors, spanning over four decades of research on fundamental interactions and an im- pressive spectrum of interests, ranging from subnuclear physics to cosmology. We think that it should be easy for the specialized reader to find out his/her preferred topic, and to jump directly to his/her field of interest. We also hope, however, that he/she will be tempted to deviate from this preferred path for enjoying the exploration of other branches of theoretical physics, and learn- ing about their historical development, following the excellent introductions written by leading experts in the field. To conclude this short introduction we would like to present our warmest thanks to Gabriele Veneziano, teacher and friend, for so many years of en- joyable and rewarding collaboration. We wish him, also on behalf of the other contributors to this volume and of all his friends, a happy 65th Birth- day, and many future years full of exciting research projects and outstanding achievements.

Bari and Bhubaneswar, Maurizio Gasperini March 2007 Jnan Maharana Contents

Part I Introduction

Gabriele Veneziano: A Concise Scientific Biography and an Interview M. Gasperini, J. Maharana ...... 3 1 Biographical Notes ...... 3 2 List of Collaborators of Gabriele Veneziano (Updated to 2006) ...... 10 3 An Interview with Gabriele Veneziano ...... 11 References ...... 16 An Unpublished Draft by Gabriele Veneziano (1973): “Non-local Field Theory Suggested by Dual Models” G. Veneziano ...... 29 1 Introduction and Content of the Paper ...... 29 2 Yukawa’sNon-localFieldTheory...... 31 3 The Zero Slope (Local) Limit of Dual Models ...... 34 4 The Correspondence Principle ...... 37 5 Non-Local,ClassicalFieldTheory...... 40 6 SmearedFields...... 41 References ...... 43

Part II Dual Resonance Models and String Theory

The Birth of the Veneziano Model and String Theory H. Rubinstein ...... 47 1 The Weizmann Institute in January 1966 and the Work Leading to the Veneziano Model ...... 47 2 The Dominant Problems from 1950 to 1970 ...... 49 3 TheBreakthrough...... 54 XII Contents

4 The Early Phenomenology ...... 55 5 Conclusion ...... 56 References ...... 57 The Birth of String Theory P. Di Vecchia ...... 59 1 Introduction ...... 59 2 Construction of the N-pointAmplitude...... 64 3 Operator Formalism and Factorization ...... 72 4 The Case α0 =1 ...... 78 5 Physical States and Their Vertex Operators ...... 85 6 The DDF States and Absence of Ghosts ...... 90 7 The Zero Slope Limit ...... 94 8 Loop Diagrams ...... 97 9 FromDualModelstoStringTheory...... 107 10 Conclusions...... 114 References ...... 115 The Beginning of String Theory: A Historical Sketch P. Di Vecchia, A. Schwimmer ...... 119 1 Introduction ...... 119 2 Prehistory: the Discovery of the Dual Scattering Amplitudes ...... 120 3 The String World Sheet Through Factorization of the N-point amplitudes ...... 125 4 The Virasoro Conditions ...... 128 5 The Critical Dimension ...... 132 6 Conclusions...... 134 References ...... 135 The Little Story of an Algebra M. A. Virasoro ...... 137 1 Introduction ...... 137 2 TheContext...... 137 References ...... 143

Part III Perturbative QCD

Parton Densities: A Personal Retrospective R. Petronzio ...... 147 References ...... 149 Infrared-sensitive Physics in QCD and in Electroweak Theory M. Ciafaloni ...... 151 1 Infrared-sensitive Observables ...... 151 2 QCD Form Factors, Multiplicities, Preconfinement ...... 153 Contents XIII

3 Inclusive Electroweak Double Logarithms ...... 155 References ...... 157 From QCD Lagrangian to Monte Carlo Simulation G. Marchesini ...... 159 1 The Status ...... 159 2 Structure of Monte Carlo generator ...... 160 3 TheLongWaytoMonteCarlo ...... 161 4 Multi-gluon Soft Distributions ...... 168 5 Monte Carlo Simulation for Soft Emission ...... 174 6 FromPartonstoHadrons ...... 176 7 Conclusion ...... 177 References ...... 178 Fracture Functions L. Trentadue ...... 181 1 Introduction and Motivations ...... 181 2 Formalism and Definitions ...... 184 3 Applications and Phenomenology ...... 201 4 Jet Cross sections and Fracture Functions ...... 214 5 Conclusions...... 217 References ...... 218

Part IV Non-perturbative QCD

Coherence and Incoherence in QCD Jets Dynamics (QCD Jets and Branching Processes) A. Giovannini, R. Ugoccioni ...... 223 1 Introduction ...... 223 2 Elementary Models and Unexplained Facts in Multiparticle Dynamics in the Early 1970s ...... 224 3 KUV Differential Evolution Equations and the Advent of QCD in the Late 1970s ...... 225 4 The Collaboration with L´eon Van Hove, and the UA5 Collaboration Results at CERN pp¯ Collider on Multiplicity Distributions, in Full Phase Space and in Restricted Pseudo-rapidity Windows ...... 228 5 New Experimental Findings on Final Charged Particle MD in e+e− Annihilation at LEP c.m. Energy, and More Precise Measurements on Final Particle MD at pp¯ Collider Top c.m. Energy. The Occurrence of Substructures or Components in the Various Collisions ...... 231 6 New Physics at CERN. The Weighted Superposition of Three Classes of Events (Soft, Semihard, and Hard) in pp Collisions at LHC ...... 233 References ...... 233 XIV Contents

The U (1)A Anomaly and QCD Phenomenology G. M. Shore ...... 235 1 Introduction ...... 235 2TheU(1)A Anomaly and the Topological Susceptibility ...... 237 3‘U(1)A WithoutInstantons’ ...... 245 4 Pseudoscalar Mesons ...... 252 5 Topological Charge Screening and the ‘Proton Spin’ ...... 265 γ 6 Polarised Two-photon Physics and a Sum Rule for g1 ...... 279 References ...... 285 Planar Equivalence 2006 A. Armoni, M. Shifman ...... 289 1 Planar Equivalence: a Refined Proof ...... 290 2 The Orientifold Large-N Expansion ...... 293 3 Applications for One-flavor QCD ...... 294 4 Applications for Three-flavor QCD ...... 295 5 Sagnotti’s Model and the Gauge/String Correspondence ...... 297 6 Charge Conjugation and the Validity of Planar Equivalence ...... 297 7 OtherDevelopments...... 298 References ...... 299

Part V Supersymmetric Gauge Theories

Instantons and Supersymmetry M. Bianchi, S. Kovacs, G. Rossi ...... 303 1 Introduction ...... 303 2 Generalities about Instantons ...... 306 3 Chiral and Supersymmetric Ward–Takahashi Identities ...... 315 4 InstantonCalculus ...... 321 5 The Effective Action Approach ...... 334 6 N = 2 SYM: Introduction ...... 348 7 N = 2 SYM: Generalities ...... 349 8 Seiberg–Witten Analysis ...... 352 9 Checking the SW Formula by Instanton Calculations...... 358 10 Topological Twist and Non-commutative Deformation...... 364 11 (Constrained) Instantons from Open Strings ...... 374 12 Instanton Effects in N =4SYM ...... 385 13 N = 4 Supersymmetric Yang–Mills Theory ...... 386 14 Instanton Calculus in N =4SYM...... 390 15 One-instanton in N = 4 SYM with SU(Nc)GaugeGroup...... 394 16 Generalisation to Multi-instanton Sectors ...... 405 17 AdS/CFT Correspondence: a Brief Overview ...... 407 Contents XV

18 Instanton Effects in the AdS/CFT Duality ...... 412 19 Conclusions...... 436 References ...... 463 The Magnetic Monopoles Seventy-five Years Later K. Konishi ...... 471 1 Color Confinement ...... 472 2 Difficulties with the Semiclassical “Non-Abelian Monopoles” ...... 474 3 Non-Abelian Monopoles from Vortex Moduli ...... 480 4 N = 2 Supersymmetric Gauge Theories and Light Non-Abelian Monopoles...... 482 5 Vortices...... 494 6 TheModel ...... 500 7 Confinement Near Conformal Vacua ...... 507 8 Quantum Chromodynamics ...... 508 9 ConclusiveRemarks...... 509 References ...... 519

Part VI String dualities and symmetries

Novel Symmetries of String Theory J. Maharana ...... 525 1 Introduction ...... 525 2 Hamiltonian Formalism and BRS Quantization ...... 527 3 Canonical Transformations and Invariance Properties of Σ ...... 534 4 Symmetries of Massive String Excitations ...... 542 5 Summary and Conclusions ...... 549 References ...... 551 Threshold Effects Beyond the Standard Model T. R. Taylor ...... 553 1 Introduction ...... 553 2 ThresholdEffectsofExtraDimensions...... 553 3 Superstring Threshold Corrections ...... 556 References ...... 559 Dualities in String Cosmology K. A. Meissner ...... 561 1 Introduction ...... 561 2 Scale Factor Duality ...... 563 3 O(d, d)SymmetrytotheLowestOrder...... 564 4 O(d, d)SymmetrytotheNextOrder...... 567 5 Discussion...... 569 References ...... 570 XVI Contents

Spontaneous Breaking of Space–Time Symmetries E. Rabinovici ...... 573 1 Introduction ...... 573 2 SpontaneousBreakingofSpaceSymmetries...... 574 3 Spontaneous Breaking of Time-Translational Invariance and of Supersymmetry...... 590 4 Spontaneous Breaking of Conformal Invariance ...... 597 5 O(N) Vector Models in d = 3: Spontaneous Breaking of Scale Invariance and the Vacuum Energy ...... 599 References ...... 604

Part VII String/Quantum Gravity, Black Holes and Entropy

The Information Paradox D. Amati ...... 609 1 Introduction ...... 609 2 StringTheoriesandBlackHoles...... 610 3 The Role of Decoherence ...... 612 4 High-energy Collisions in String Theory and Metric Back Reaction . 613 5 Metric Back Reaction and Possible Avoidance of Black Holes ...... 615 6 ConclusionsandOutlook...... 615 References ...... 616 Cosmological Entropy Bounds R. Brustein ...... 619 1 ToGabriele...... 619 2 Introduction ...... 619 3 TheCausalEntropyBound...... 624 4 The Generalized Second Law and the Causal Entropy Bound ...... 645 5 Area Entropy, Entanglement Entropy and Entropy Bounds ...... 655 References ...... 658 Extremal Black Holes in Supergravity L. Andrianopoli, R. D’Auria, S. Ferrara, M. Trigiante ...... 661 1 Introduction: Extremal Black Holes from Classical General Relativity to String Theory ...... 661 2 Extremal Black Holes as Massive Representations ofSupersymmetry...... 668 3 The General Form of the Supergravity Action in Four Dimensions and its BPS Configurations ...... 674 4 Supersymmetric Black Holes: General Discussion ...... 694 5 BPS and Non-BPS Attractor Mechanism: The Geodesic Potential . . 701 6 Detailed Analysis of Attractors in Extended Supergravities: BPS and Non-BPS Critical Points ...... 713 7 Conclusions...... 723 References ...... 724 Contents XVII

Expectation Values and Vacuum Currents of Quantum Fields G. A. Vilkovisky ...... 729 1 Introduction ...... 729 2 Lecture1...... 730 3 Lecture2...... 741 4 Lecture3...... 752 5 Lecture4...... 768 References ...... 783

Part VIII String Cosmology

Dilaton Cosmology and Phenomenology M. Gasperini ...... 787 1 Dilaton-dominated Inflation: the Pre-big Bang Scenario ...... 789 2 The Relic Dilaton Background ...... 812 3 Late-time Cosmology: Dilaton Dark Energy ...... 826 References ...... 842 Relic Gravitons and String Pre-big-bang Cosmology A. Buonanno, C. Ungarelli ...... 845 1 Introduction ...... 845 2 Graviton Production in Cosmology ...... 847 3 Gravitational-wave Background in Pre-big-bang Inflation ...... 853 4 Accessibility of LIGO to Pre-big-bang Models ...... 857 5 Conclusions...... 859 References ...... 860 Magnetic Fields, Strings and Cosmology M. Giovannini ...... 863 1 Half a Century of Large-Scale Magnetic Fields ...... 863 2 Magnetogenesis ...... 869 3 Why String Cosmology? ...... 892 4 Primordial or Not Primordial, This Is the Question...... 902 5 ConcludingRemarks...... 934 References ...... 935 Cosmological Singularities and a Conjectured Gravity/Coset Correspondence T. Damour ...... 941 1 Introduction ...... 941 2 Cosmological Billiards ...... 942 3 Gravity/Coset Correspondence ...... 944 4 A New View of the (quantum) Fate of Space at a Cosmological Singularity...... 946 References ...... 948 XVIII Contents

Brane Inflation: String Theory Viewed from the Cosmos S.-H. H. Tye ...... 949 1 Introduction ...... 949 2 Brane Inflation ...... 956 3 GracefulExit...... 961 4 Production and Properties of Cosmic Superstrings ...... 964 5 Evolution and Detection of Cosmic Superstrings ...... 966 6 Remarks...... 970 References ...... 972