String Theory Demystified

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|NS〉 ⊕ |NS〉 Sector, 203 |NS〉 ⊕ |R〉 Sector, 204 |R〉 ⊕ |NS〉 Sector, 204 |R〉 ⊕ |R〉 Sector, 204 3D-branes, 16 25th dimension, compactifi cation of, 153–155 A Abbott, Edward, 16 Action for heterotic SO(32) string theory, 208–209 Action principle, 23, 32 AdS/CFT (anti-de Sitter/conformal fi eld theory) correspondence, 257, 260–261 Analytic functions, 100 Anisotropic Kasner metric, 269 Annihilation operators, 76 Anomalies, 121, 123 Anticommutation relations, 144, 146 Anticommuting Grassman variables, 171–173 Anti-de Sitter universe, 266 Anti-de Sitter/conformal fi eld theory (AdS/CFT) correspondence, 257, 260–261 Antiholomorphic functions, 97 Antiperiodic fermions, 213 Antiperiodic sector A, 209–210 Antiquark, 231 Auxiliary fi elds, 26 B Bardeen, James, 246 Big bang theory, 265 Bispinors, 200 Black holes charged, 243–245 computing temperature of, 247–248 entropy calculations for, 249–253 in general relativity, 240–243 laws of mechanics, 246–247 overview, 239–240 INDEX Copyright © 2009 by The McGraw-Hill Companies, Inc. Click here for terms of use. Bosonic string theory. See also BRST quantization; D-branes; Equations of motion; String quantization; Worldsheet currents defi ned, 14, 188–189 ground state of, 81–82, 188 open strings, 162 overview, 21–22 Bosonization, 200–201 Bosons canonical quantization, 184–185 contribution to normal ordering constant, 213–214 defi ned, 5 energy-momentum tensor, 138–139 heterotic string theory, 215–216 Higgs, 8 Nambu-Goldstone, 230 particle classes, 127 periodic, 213 space-time, 143, 199–200 spin-1 gauge, 8 spin-2, 8–9 states of in Type II theories, 204 Boundary conditions closed string, 33, 142 Dirichlet, 33, 47, 164, 223–224 Neumann, 33, 44–45, 164, 223 Neveau-Schwarz, 141, 145, 195–196, 198–200 open string, 32–33, 141, 224f overview, 140 Ramond, 141, 146–147, 195–198 Brane ripples, 276 Branes. See also D-branes cosmological models based on, 270 D0, 165, 176 D1, 165 D3, 165 Dp, 221 ekpyrotic universe, 275–278 hidden, 273 overview, 15–16 299
300 String Theory Demystifi ed Branes (Cont.): p, 15 Randall-Sundrum model, 273–275 space-fi lling, 221 three-dimensional, 16 visible, 273 BRST quantization invariant states, 118–120 no-ghost theorem, 125 operators, 116–118 overview, 115 in string theory-CFT, 120–121 transformations, 121–125 Bulk, 16, 222, 273 C Calabi-Yau manifold, 17 Canonical quantization, 144, 184–185 Carter, Brandon, 246 Cauchy-Riemann equations, 100 Central charge, 80 Central extension, 104 CFT (conformal fi eld theory) AdS/CFT correspondence, 257, 260–261 BRST in, 120–121 central extension, 104 closed string, 105–107 complex coordinates, 94–97 generators of conformal transformations, 98–100 operator product expansion, 110–113 overview, 89–92 role of in string theory, 92–93 two-dimensional conformal group, 100–104 Wick expansion, 107–110 Wick rotations, 93 Chan-Paton factors, 191, 231 Charged black holes, 243–245 χ (Euler characteristic), 36–39 Chiral conformal fi eld theories, 93 Christoffel symbols, 241 Closed strings bosonic string theory, 188–189 boundary conditions, 33, 142 classical string theory, 46–47 commutation relations for, 74–75 conformal fi eld theory, 105–107 mode expansions, 142–143 spectrum, 82–85 in string theory, 13f T-duality and, 159–161 and worldsheets, 29f Commutation relations for closed strings, 74–75 deriving for modes, 73 for open strings, 75 R sector, 146 Compactifi cation. See also T-duality of 25th dimension, 153–155 D-branes, 164–165 heterotic string theory, 216–219 higher dimensions, 16, 17f modifi ed mass spectrum, 155–158 and M-theory, 15 overview, 153 Complex coordinates, 94–97 Conformal anomaly, 121 Conformal dimensions, 111 Conformal fi eld theory (CFT) AdS/CFT correspondence, 257, 260–261 BRST in, 120–121 central extension, 104 closed string, 105–107 complex coordinates, 94–97 generators of conformal transformations, 98–100 operator product expansion, 110–113 overview, 89–92 role of in string theory, 92–93 two-dimensional conformal group, 100–104 Wick expansion, 107–110 Wick rotations, 93 Conformal fi elds, 110 Conformal group, two-dimensional, 100 Conformal transformations, 89, 98–100 Conformal weights, 111 Conformally fl at metrics, 90 Conjugate momentum, 33–34 Conserved worldsheet currents, 133–136 Coordinates boundary conditions, 224 complex, 94–97 conventions for, 22 DD, 224–226 fermionic, 168–169, 176, 184–185 light-cone, 39–43 NN, 224 space-time, 175–176 string, 30 Cosmology brane worlds, 275–278 Einstein’s equations, 266 ekpyrotic universe, 275–278 infl ation, 266–268 Kasner metric, 268–273 overview, 265 Randall-Sundrum model, 273–275 Covariant quantization advantages of, 115 closed string spectrum, 82–85 commutation relations, 74–75 open string spectrum, 75–82 overview, 70–73 Creation operator, 76 Critical bosonic string theory, 82 Critical dimension bosonic string theory, 82 RNS superstrings, 149–150 Critical mass density, 267 Currents, worldsheet. See Worldsheet currents Curvature constant K, 266 Curved space-time, 3
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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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Page 312 and 313: Books References Becker, K., M. Bec
Page 316 and 317: INDEX 301 Cyclic model, 277 Cylinde
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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