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Gabriele Veneziano (Updated to 2006) ...... 10 3 An Interview with Gabriele Veneziano ...... 11 References ...... 16 An Unpublished Draft by Gabriele Veneziano (1973): “Non-local Field Theory Suggested by Dual Models” G. Veneziano ...... 29 1 Introduction and Content of the Paper ......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