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  • Demystified Series

    Accounting DemystifiedAdvanced Calculus DemystifiedAdvanced Physics DemystifiedAdvanced Statistics DemystifiedAlgebra DemystifiedAlternative Energy DemystifiedAnatomy DemystifiedAstronomy DemystifiedAudio DemystifiedBiochemistry DemystifiedBiology DemystifiedBiotechnology DemystifiedBusiness Calculus DemystifiedBusiness Math DemystifiedBusiness Statistics DemystifiedC++ DemystifiedCalculus DemystifiedChemistry DemystifiedCircuit Analysis DemystifiedCollege Algebra DemystifiedComplex Variables DemystifiedCorporate Finance DemystifiedDatabases DemystifiedDiabetes DemystifiedDifferential Equations DemystifiedDigital Electronics DemystifiedDiscrete Mathematics DemystifiedEarth Science DemystifiedElectricity DemystifiedElectronics DemystifiedEngineering Statistics DemystifiedEnvironmental Science DemystifiedEveryday Math Demystified Fertility DemystifiedFinancial Planning DemystifiedForensics DemystifiedFrench DemystifiedGenetics DemystifiedGeometry DemystifiedGerman DemystifiedGlobal Warming and Climate Change DemystifiedHedge Funds DemystifiedInvesting DemystifiedItalian DemystifiedJava Demystified

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  • String Theory Demystifi ed

    David McMahon

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    Preface xi

    CHAPTER 1 Introduction 1A Quick Overview of General Relativity 2A Quick Primer on Quantum Theory 3The Standard Model 8Quantizing the Gravitational Field 8Some Basic Analysis in String Theory 10Unifi cation and Fundamental Constants 11String Theory Overview 12Summary 18Quiz 18

    CHAPTER 2 The Classical String I: Equations of Motion 21The Relativistic Point Particle 22Strings in Space-Time 28Equations of Motion for the String 32The Polyakov Action 36Mathematical Aside: The Euler Characteristic 36Light-Cone Coordinates 39Solutions of the Wave Equation 43Open Strings with Free Endpoints 44Closed Strings 46

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  • Open Strings with Fixed Endpoints 47Poisson Brackets 49Quiz 49

    CHAPTER 3 The Classical String II: Symmetries and Worldsheet Currents 51

    The Energy-Momentum Tensor 52Symmetries of the Polyakov Action 53Transforming to a Flat Worldsheet Metric 59Conserved Currents from Poincar Invariance 63The Hamiltonian 67Summary 67Quiz 67

    CHAPTER 4 String Quantization 69Covariant Quantization 70Light-Cone Quantization 85Summary 87Quiz 87

    CHAPTER 5 Conformal Field Theory Part I 89The Role of Conformal Field Theory

    in String Theory 92Wick Rotations 93Complex Coordinates 94Generators of Conformal Transformations 98The Two-Dimensional Conformal Group 100Central Extension 104Closed String Conformal Field Theory 105Wick Expansion 107Operator Product Expansion 110Summary 114Quiz 114

    CHAPTER 6 BRST Quantization 115BRST Operators and Introductory Remarks 116BRST-Invariant States 118

    vi String Theory Demystifi ed

  • BRST in String Theory-CFT 120BRST Transformations 121No-Ghost Theorem 125Summary 125Quiz 126

    CHAPTER 7 RNS Superstrings 127The Superstring Action 128Conserved Currents 133The Energy-Momentum Tensor 136Mode Expansions and Boundary Conditions 140Super-Virasoro Generators 143Canonical Quantization 144The Super-Virasoro Algebra 145The Open String Spectrum 147GSO Projection 148Critical Dimension 149Summary 150Quiz 150

    CHAPTER 8 Compactifi cation and T-Duality 153Compactifi cation of the 25th Dimension 153Modifi ed Mass Spectrum 155T-Duality for Closed Strings 159Open Strings and T-Duality 162D-Branes 164Summary 165Quiz 165

    CHAPTER 9 Superstring Theory Continued 167Superspace and Superfi elds 168Superfi eld for Worldsheet Supersymmetry 171Grassman Integration 173A Manifestly Supersymmetric Action 174The Green-Schwarz Action 175Space-Time Supersymmetry and Strings 180

    Contents vii

  • Light-Cone Gauge 181Canonical Quantization 184Summary 185Quiz 186

    CHAPTER 10 A Summary of Superstring Theory 187A Summary of Superstring Theory 187Superstring Theory 190Dualities 192Quiz 193

    CHAPTER 11 Type II String Theories 195The R and NS Sectors 195The Spin Field 200Type II A String Theory 201Type II B Theory 203The Massless Spectrum of Different Sectors 203Summary 204Quiz 205

    CHAPTER 12 Heterotic String Theory 207The Action for SO(32) Theory 208Quantization of SO(32) Theory 209The Spectrum 214Compactifi cation and Quantized Momentum 216Summary 219Quiz 219

    CHAPTER 13 D-Branes 221The Space-Time Arena 223Quantization 225D-Branes in Superstring Theory 230Multiple D-Branes 230Tachyons and D-Brane Decay 235Summary 237Quiz 237

    viii String Theory Demystifi ed

  • CHAPTER 14 Black Holes 239Black Holes in General Relativity 240Charged Black Holes 243The Laws of Black Hole Mechanics 246Computing the Temperature of a Black Hole 247Entropy Calculations for Black Holes

    with String Theory 249Summary 253Quiz 253

    CHAPTER 15 The Holographic Principle