String Theory Demystified

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INDEX 303 Mechanics, quantum. See Quantum theory Metric tensor, 3 Metrics conformally fl at, 90 defi ned, 2–3 describing distance measurements with, 23 Euclidean, 93 fi ducial, 59 induced, 30–31 Kasner, 268–273 Minkowski, 23, 40, 60, 144 Robertson-Walker, 266 Schwarzschild, 242 signature of, 23 transforming worldsheet currents to fl at, 59–63 Minkowski metric, 23, 40, 60, 144 Möbius strip, 37f Möbius transformation, 102 Mode expansions closed string, 142–143 open string, 141–142 overview, 140 Modifi ed mass spectrum, 155–158 Momentum density, 66 Momentum mode, 155 Motion. See Equations of motion M-theory, 15, 192, 258–260 Multiple D-branes, 230–234 Muons, 17 N Naked singularity, 244 Nambu-Goldstone bosons, 230 Nambu-Goto action, 32 Negative mass, 81 Neumann boundary conditions equations of motion for string, 33 open strings with free endpoints, 44–45 space-time arena, 223 and T-duality, 164 Neveau-Schwarz (NS) boundary conditions, 141, 145, 195–196, 198–200 Nilpotent of degree two, 117 NN coordinates, 224 Noether currents, 63–66 Noether’s theorem, 53–55, 137 No-ghost theorem, 125 Nonabelian gauge theory, 208 Non-euclidean geometry, 2–3 Normal ordering, 78, 108 NS (Neveau-Schwarz) boundary conditions, 141, 145, 195– 196, 198–200 Nuclear particle interactions, 8 Null states, 119 Number operators, 76 O One-dimensional strings, 10f OPE (operator product expansion), 110–113 Open strings in bosonic string theory, 188–189 boundary conditions, 32–33, 141, 224f commutation relations for, 75 defi ned, 13f with fi xed endpoints, 47–48 with free endpoints, 44–46 modal expansion, 141–142, 225 RNS superstrings, 147–148 spectrum, 75–82 T-duality and, 162–164 Operator product expansion (OPE), 110–113 Operators BRST quantization, 116–118 fermion number, 148 ghost number, 117 Klein, 149 lowering, 78 parity, 148–149 raising, 78 string quantization, 76 super-Virasoro NS sector algebra, 145 overview, 143–144 R sector algebra, 146–147 total number, 77, 197 Virasoro, 78, 80, 155–156 Opposite chirality, 201 Oriented strings, 188–189 Outer horizon, 244 P Parity operators, 148–149 Particles classes of, 127 distinct, 156 families of, 17 heterotic string theory, 215 interactions of, 6f, 8 point, 10f, 13f, 165, 176–179 and postulated super-partners, 190t quantum fi eld theory versus string theory, 10f in quantum theory, 4–6 relativistic point, 22–28, 176 in string theory, 12–14 Pauli exclusion principle, 5 p-brane, 15 Penrose, Roger, 244 Periodic bosons, 213 Periodic fermions, 213 Periodic sector P, 209–210 Perturbative expansion, 6 Photon, 7f, 229 Physical states, 118–119 Planck length, 11–12, 250 Planck mass, 12 Planck scale, 13 Planck time, 12 Poincaré invariance, 63–66 Poincaré transformations, 56–57
304 <strong>String</strong> <strong>Theory</strong> Demystifi ed Point particles, 10f, 13f, 165, 176–179 Poisson brackets, 49 Polyakov action light-cone coordinates, 42 overview, 36 symmetries of overview, 53–56 Poincaré transformations, 56–57 reparameterizations, 57–58 Weyl transformations, 58–59 Potential, 235f Primary fi elds, 110 Propagators, 107 Q QCD (quantum chromodynamics), 231 Quanta, 5 Quantization BRST invariant states, 118–120 no-ghost theorem, 125 operators, 116–118 overview, 115 in string theory-CFT, 120–121 transformations, 121–125 canonical, 144, 184–185 covariant advantages of, 115 closed string spectrum, 82–85 commutation relations, 74–75 open string spectrum, 75–82 overview, 70–73 D-branes, 225–230 fi rst, 69 heterotic SO(32) string theory, 209–214 light-cone, 85–87, 115 overview, 69 second, 69 Quantized momentum, 216–219 Quantum chromodynamics (QCD), 231 Quantum fi eld theory, 5–8, 10f Quantum of gravitational fi eld, 8–10 Quantum theory basics of, 3–8 overview, 1–2 Quark, 231 R R (Ramond) boundary conditions, 141, 146–147, 195–198 Radial ordering, 111 Radiation, 240 Radion fi eld, 275 Raising operators, 78 Ramond (R) boundary conditions, 141, 146–147, 195–198 Ramond-Neveu-Schwarz (RNS) superstrings boundary conditions closed string, 142 open string, 141 overview, 140 canonical quantization, 144 conserved currents, 133–136 critical dimension, 149–150 energy-momentum tensor, 136–139 GSO projection, 148–149 Majorana spinors, 130–132 mode expansions closed string, 142–143 open string, 141–142 overview, 140 open string spectrum, 147–148 overview, 127–129 supersymmetry transformations on worldsheet, 132–133 super-Virasoro operators NS sector algebra, 145 overview, 143–144 R sector algebra, 146–147 Randall, Lisa, 273 Randall-Sundrum model, 273–275 Reissner-Nordström black holes, 243 Relativistic point particles, 22–28, 176 Renormalization, 8 Reparameterizations, 57–58 Rescaling, Weyl, 58–59 Ricci tensor, 241 Riemann curvature tensor, 241 Right moving antiholomorphic functions, 97 Right-moving sector, 197, 207, 209 Ripples, brane, 276 RNS (Ramond-Neveu-Schwarz) superstrings boundary conditions closed string, 142 open string, 141 overview, 140 canonical quantization, 144 conserved currents, 133–136 critical dimension, 149–150 energy-momentum tensor, 136–139 GSO projection, 148–149 Majorana spinors, 130–132 mode expansions closed string, 142–143 open string, 141–142 overview, 140 open string spectrum, 147–148 overview, 127–129 supersymmetry transformations on worldsheet, 132–133 super-Virasoro operators NS sector algebra, 145 overview, 143–144 R sector algebra, 146–147 Robertson-Walker metric, 266 S Scale factor, 266 Scale invariant, 91 Scale transformation, 91–92 Schrödinger’s equation, 4 Schwarzschild black hole, 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 3 fl at spac
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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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CHAPTER 14 Black Holes 251 Recallin
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Page 312 and 313: Books References Becker, K., M. Bec
Page 314 and 315: |NS〉 ⊕ |NS〉 Sector, 203 |NS
Page 316 and 317: INDEX 301 Cyclic model, 277 Cylinde
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String Theory Demystified

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