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of Gabriele Veneziano (Updated to 2006) . 10 3 An Interview with Gabriele Veneziano . 11 References . 16 An Unpublished Draft by Gabriele Veneziano (1973): “Non-local Field Theory Suggested by Dual Models” G. Veneziano .................................................... 29 1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