String Theory Demystified

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INDEX 301 Cyclic model, 277 Cylinders, 37 D D0-brane, 165, 176 D1-brane, 165 D3-brane, 165 D-branes compactifi cation, 164–165 multiple, 230–234 overview, 221–222 quantization, 225–230 space-time arena, 223–224 in string theory, 15–16 in superstring theory, 230 tachyons and decay, 235–237 DD coordinates, 224–226 De Sitter universe, 266 Decay, D-brane, 235–237 Diffeomorphism, 57–58 Dilaton, 85, 188 Dimensions compactifi cation, 153–155 conformal, 111 critical bosonic string theory, 82 RNS superstrings, 149–150 higher, 16–17 spatial, 188 Dirac delta function, 71 Dirichlet boundary conditions equations of motion for string, 33 open strings with fi xed endpoints, 47 space-time arena, 223–224 and T-duality, 164 Distinct particles, 156 Dp-branes, 221. See also D-branes Dualities overview, 15 S-duality, 193 T-duality for closed strings, 159–161 D-branes, 164–165 open strings and, 162–164 overview, 192–193 E E 8 × E 8 theory, 192 Einstein fi eld equations, 266 Einstein’s equation, 3 Ekpyrotic temperature, 276 Ekpyrotic universe, 275–278 Electromagnetic interactions, 8 Electron-positron pair, 7f Electrons, heavy, 17 Electroweak theory, 232 Endpoints, dual string, 164 Energy-momentum tensor, 3, 52, 106, 136–139 Entropy, 249–253, 257 Equal-time anticommutation relations, 184 Equations of motion closed strings, 46–47 Euler characteristic, 36–39 light-cone coordinates, 39–43 open strings with fi xed endpoints, 47–48 with free endpoints, 44–46 overview, 21–22 Poisson brackets, 49 Polyakov action, 36 relativistic point particle, 22–28 for string, 32–35 strings in space-time, 28–32 wave equation solutions, 43–44 Euclidean metrics, 93 Euclidean quantum fi eld theories, 90 Euler characteristic (χ), 36–39 Euler-Lagrange equations, 39, 55 Event horizon, 242 Extremal black hole, 245 F Families of particles, 17 Fermion number operators, 148 Fermionic coordinates, 168–169, 176, 184–185 Fermionic fi elds, 116 Fermions, 5, 8, 22, 127, 138. See also RNS superstrings; Supersymmetry Feynman diagram, 6–7 Fiducial metric, 59 Fine structure constant, 11 First quantization, 69 Five-dimensional black holes, 249 Five-dimensional gravity, 257 Fixed point boundary conditions equations of motion for string, 33 open strings with fi xed endpoints, 47 space-time arena, 223–224 and T-duality, 164 Flat metrics, 59–63 Flatness problem, 267 Fluctuations, brane, 276 Fock space, 76, 197, 201 Force-mediating particles, 127 Fourier expansion, 49 Free endpoint boundary conditions equations of motion for string, 33 open strings with free endpoints, 44–45 space-time arena, 223 and T-duality, 164 Free point particles, 22–28, 176 Fundamental constants, 11–12 Fundamental particles, 13f G Gamma matrices, 197–198 Gauge freedom, 59 General relativity (GR), 1–3, 240–243
302 <strong>String</strong> <strong>Theory</strong> Demystifi ed Generators of conformal transformations, 98–100 Geometry, non-euclidean, 2–3 Ghost number operator U, 117 Ghost states, 115 Ghost vacuum state, 124 Gliozzi-Scherk-Olive (GSO) projection, 148–149, 195 Global internal symmetries, 57 Global symmetries, 53, 131 GR (general relativity), 1–3, 240–243 Grassman coordinates, 168–169, 176, 184–185 Grassman integration, 173–174 Grassman numbers, 132 Gravitational constants, 10 Gravitational fi elds Einstein’s equation, 3 quantizing, 8–10 Gravitational scalar fi eld, 188 Gravitons, 8–9, 15–16, 85 Gravity and bosonic string theory, 188 and D-branes, 222 fi ve-dimensional, 257 Green-Schwarz action, 175–179 Ground state bosonic string theory, 81, 188 D-branes, 228–229 GS formalism, 212 GSO (Gliozzi-Scherk-Olive) projection, 148–149, 195 H Half-integral spin, 22 Hamiltonian, 67 Harmonic oscillator, 76 Hawking, Stephen, 239–240, 244 Heavy electrons, 17 Heterotic string theory compactifi cation, 216–219 defi ned, 15 E 8 × E 8 theory, 192 overview, 187, 207–208 quantized momentum, 216–219 SO(32) theory action for, 208–209 overview, 192 quantization of, 209–214 spectrum of, 214–216 Hidden brane, 273 Hierarchy problem of particle physics, 273 Higgs boson, 8 Higher dimensions, 16–17 Holographic principle AdS/CFT correspondence, 257, 260–261 and M-theory, 258–260 overview, 255–257 Holomorphic functions, 97 Homeomorphism, 36–37 Homogeneity, 267 Horizon, 242 Hubble constant, 266, 271 I Induced metrics, 30–31 Infi nities, 7 Infl ation, 266–268 Instantons, 230 Integral spin, 22 Interactions in particle physics, 6f Intrinsic distance, 51 Invariant states, BRST, 118–120 IR-UV connection, 261 Isotropic space, 266 Isotropy, 267 J Janna, Levin, 270 Johnson, Clifford V., 237 K Kaluza-Klein excitation number, 158 Kappa symmetry, 180 Kasner conditions, 269 Kasner metric, 268–273 Kerr black holes, 243 Klein bottle, 37f Klein operators, 149 L Lagrangian, 26 Large Hadron Collider (LHC), 190 Laws of black hole mechanics, 240, 246–247 Left moving holomorphic functions, 97 Left-moving modes, GS formalism, 212 Left-moving sector, 197, 207 Level matching condition, 84, 157–158 LHC (Large Hadron Collider), 190 Lie algebra, 116 Light-cone coordinates, 39–43 Light-cone gauge, 181–184, 216 Light-cone quantization, 85–87, 115 Local symmetries, 53 Loop integral, 7 Lorentz invariance, 85, 150 Lowercase letters in coordinates, 22 Lowering operators, 78 M Majorana condition, 142 Majorana spinors, 130–132 Majorana-Weyl fermions, 209 Majorana-Weyl spinors, 198 Maldacena, Juan, 258 Massive states, 147 Massless spectrum of sectors, 203–204 Massless vector state, 189 Matter particles, 127 Maxwell equations, 54 Measurable observables, 4 Mechanics, laws of black hole, 240, 246–247
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Accounting Demystified Advanced Cal
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Copyright © 2009 by The McGraw-Hil
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For more information about this tit
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Contents vii BRST in String Theory-
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Contents ix CHAPTER 14 Black Holes
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PREFACE String theory is the greate
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Preface xiii time as this one to he
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CHAPTER 1 Introduction General rela
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CHAPTER 1 Introduction 5 we say tha
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CHAPTER 1 Introduction 7 initial an
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CHAPTER 1 Introduction 9 a spin-2 b
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CHAPTER 1 Introduction 11 So if α
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CHAPTER 1 Introduction 13 Figure 1.
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CHAPTER 1 Introduction 15 • Type
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CHAPTER 1 Introduction 17 Close up,
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CHAPTER 1 Introduction 19 5. The mi
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CHAPTER 2 The Classical String I: E
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CHAPTER 2 Equations of Motion 23 To
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CHAPTER 2 Equations of Motion 25 No
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CHAPTER 2 Equations of Motion 29 ct
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CHAPTER 2 Equations of Motion 31 Th
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CHAPTER 2 Equations of Motion 33 is
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CHAPTER 2 Equations of Motion 35 Si
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CHAPTER 2 Equations of Motion 37 ho
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CHAPTER 2 Equations of Motion 39 Th
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CHAPTER 2 Equations of Motion 41 wh
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CHAPTER 2 Equations of Motion 43 In
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CHAPTER 2 Equations of Motion 47 We
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CHAPTER 2 Equations of Motion 49 In
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CHAPTER 3 The Classical String II:
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CHAPTER 3 Symmetries and Worldsheet
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CHAPTER 4 String Quantization At th
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CHAPTER 4 String Quantization Here,
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CHAPTER 4 String Quantization That
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CHAPTER 4 String Quantization Using
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CHAPTER 4 String Quantization expec
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CHAPTER 4 String Quantization † A
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CHAPTER 4 String Quantization To ob
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CHAPTER 4 String Quantization lower
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CHAPTER 4 String Quantization this)
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CHAPTER 4 String Quantization Norma
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CHAPTER 5 Conformal Field Theory Pa
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CHAPTER 6 BRST Quantization So far
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CHAPTER 6 BRST Quantization 117 It
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CHAPTER 6 BRST Quantization 119 Cal
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CHAPTER 6 BRST Quantization 121 The
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CHAPTER 6 BRST Quantization 123 To
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CHAPTER 6 BRST Quantization 125 The
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CHAPTER 7 RNS Superstrings The real
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CHAPTER 7 RNS Superstrings 129 EXAM
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CHAPTER 7 RNS Superstrings 131 SOLU
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CHAPTER 7 RNS Superstrings 133 In t
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CHAPTER 7 RNS Superstrings 135 Now,
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CHAPTER 7 RNS Superstrings 137 We c
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CHAPTER 7 RNS Superstrings 139 We o
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CHAPTER 7 RNS Superstrings 141 OPEN
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CHAPTER 7 RNS Superstrings 143 If w
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CHAPTER 7 RNS Superstrings 145 The
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CHAPTER 7 RNS Superstrings 147 From
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CHAPTER 7 RNS Superstrings 149 The
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CHAPTER 7 RNS Superstrings 151 3. A
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CHAPTER 8 Compactifi cation and T-D
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CHAPTER 9 Superstring Theory Contin
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CHAPTER 10 A Summary of Superstring
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CHAPTER 11 Type II String Theories
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CHAPTER 12 Heterotic String Theory
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CHAPTER 13 D-Branes One of the most
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CHAPTER 13 D-Branes 223 The Space-T
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CHAPTER 13 D-Branes 225 Once again
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CHAPTER 13 D-Branes 227 and ( X i i
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CHAPTER 13 D-Branes 229 fi rst exci
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CHAPTER 13 D-Branes 231 a set of D-
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CHAPTER 13 D-Branes 233 D-brane 1 a
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CHAPTER 13 D-Branes 235 Tachyons ca
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CHAPTER 13 D-Branes 237 We consider
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CHAPTER 14 Black Holes Black holes,
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CHAPTER 14 Black Holes 241 This equ
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CHAPTER 14 Black Holes 243 Here, G
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CHAPTER 14 Black Holes 245 When the
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CHAPTER 14 Black Holes 247 hole squ
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CHAPTER 14 Black Holes 249 Entropy
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Page 318 and 319: INDEX 303 Mechanics, quantum. See Q
Page 320 and 321: INDEX 305 Schwarzschild metric, 242
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String Theory Demystified

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