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Schwarzschild metric, 242 Schwarzschild radius, 250 Second quantization, 69 Sectors, 141. See also individual sectors by name Signatures of metrics, 23 Singularities, 241 SO(32) heterotic string theory action for, 208 209 overview, 192 quantization of, 209 214 Space- lling branes, 221 Space-time arena, 223 224 Space-time bosons, 143, 199 200 Space-time fermions, 143, 200 Space-time supersymmetry, 175 176, 180 Space-time translation, 56 57 Spatial dimensions in bosonic string theory, 188 Special conformal transformations, 99 Spin-1 gauge bosons, 8 Spin-1/2 fermions, 8 Spin-2 bosons, 8 9 Spinor index, 177 Splitting strings, 14 Standard model, 8 Standing waves on string, 45 Stress-energy tensor, 3, 52, 106, 136 139 String coordinates, 30 String quantization covariant closed string spectrum, 82 85 commutation relations for closed string, 74 75 commutation relations for open string, 75 open string spectrum, 75 82 overview, 70 73 light-cone, 85 87 overview, 69 String sigma model action de ned, 36 light-cone coordinates, 42 symmetries of overview, 53 56 Poincar transformations, 56 57 reparameterizations, 57 58 Weyl transformations, 58 59 String theory. See also individual types of string theory by name; Superstring theory basic analysis in, 10 11 BRST quantization in, 120 121 conformal eld theory in, 92 93 D-branes, 15 16 fundamental constants, 11 12 general relativity, 2 3 higher dimensions, 16 17 M-theory, 15 overview, 1 2, 12 14 quantizing gravitational eld, 8 10 quantum theory, 3 8 standard model, 8 types of, 14 15 uni cation, 11 12
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Strings in space-time, 28 32 Strong particle interactions, 8 Structure constants, 116 Sundrum, Raman, 273 Super Yang-Mills (SYM) theory, 257, 259 261 Supercharge, 169 Supercovariant derivative, 171 Supercurrents, 138 Super elds overview, 168 171 for worldsheet supersymmetry, 171 173 Super-partners, 190 Super-Poincar group, 178 Superspace, 168 171 Superstring theory. See also RNS superstrings; Type II A string theory; Type II B string theory bosonic string theory, 188 189 canonical quantization, 184 185 D-branes in, 230 dualities, 192 193 Grassman integration, 173 174 Green-Schwarz action, 175 179 heterotic E8 E8, 192 heterotic SO(32), 192 light-cone gauge, 181 184 overview, 167 168, 187 188, 190 191 space-time supersymmetry, 180 super elds overview, 168 171 for worldsheet supersymmetry, 171 173 superspace, 168 171 supersymmetric action, 174 175 type I, 14, 191 Supersymmetry (SUSY) de ned, 127 point particle, 176 179 space-time, 180 supersymmetric actions, 174 175 transformations, 132 133, 172 173 ways to describe, 210 Supersymmetry generator, 169 Super-Virasoro operators NS sector algebra, 145 overview, 143 144 R sector algebra, 146 147 Susskind, Leonard, 256 SUSY (supersymmetry) de ned, 127 point particle, 176 179 space-time, 180 supersymmetric actions, 174 175 transformations, 132 133, 172 173 ways to describe, 210 SYM (Super Yang-Mills) theory, 257, 259 261 Symmetries. See also Worldsheet currents energy-momentum tensor, 52 53 hamiltonian, 67 overview, 51 of Polyakov action overview, 53 56
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Symmetries, of Polyakov action (Cont.): Poincar transformations, 56 57 reparameterizations, 57 58 Weyl transformations, 58 59 Symmetry breaking, 17
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Uncertainty principle, 4, 9 Uni cation, 11 12 Unoriented strings, 188 189 Uppercase letters in coordinates, 22
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Tachyons D-brane decay and, 235 237 ground state of bosonic string theory, 81 82 GSO projection, 148 Taus, 17 Taylor expansion, 171 172 T-duality for closed strings, 159 161 D-branes, 164 165 open strings and, 162 164 overview, 192 193 Temperature of black holes, 247 248 ekpyrotic, 276 Tensors. See individual tensors by name Thermodynamics, 246 T Hooft, Gerard, 256 Three-dimensional branes, 16 Topology, 17 Torus surface, 37f Total number operators, 77, 197 Trace, calculating for energy-momentum tensor, 52 53 Transformations BRST, 121 125 conformal, 90, 98 100 M bius, 102 Poincar conserved currents from, 63 66 overview, 56 57 scale, 91 92 special conformal, 99 supersymmetry, 132 133 Weyl, 58 59 Two-dimensional conformal group, 100 104 Two-component Majorana spinors, 130 Two-dimensional conformal eld theories, 90 Two-point function, 107 Type I string theory, 14, 191 Type II A string theory de ned, 15, 191 massless spectrum of different sectors, 203 204 NS sectors, 195 196, 198 200 overview, 201 202 R sectors, 195 198 spin eld, 200 201 Type II B string theory de ned, 15, 191 massless spectrum of different sectors, 203 204 NS sectors, 195 196, 198 200 overview, 203 R sectors, 195 198 spin eld, 200 201
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Vacuum eld equations, 241 Vanishing Euler characteristic, 37 Vibration of strings, 14, 92 93 Virasoro algebra with central extension, 80, 104 Virasoro constraints, 78 Virasoro operators, 78, 80, 155 156 Virtual processes, 7 Visible branes, 273 Volume elements, 96
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Warp factor, 274 Wave equation solutions, 43 44 Wave function, 4 5 Weak particle interactions, 8 Weyl spinors, 149 Weyl transformations, 58 59 Wick expansion, 107 110 Wick rotations, 93 Winding contribution, 47 Winding mode, 154 Winding number, 47, 154 Winding states, 154 Witten algebra, 104 World line for point particle, 13f Worldsheet currents conserved currents from Poincar invariance, 63 66 energy-momentum tensor, 52 53 hamiltonian, 67 overview, 51 supersymmetry transformations on, 132 133 symmetries of Polyakov action overview, 53 56 Poincar transformations, 56 57 reparameterizations, 57 58 Weyl transformations, 58 59 transforming to at metric, 59 63 Worldsheet supersymmetry, 171 173 Worldsheet for closed strings, 13f, 29f, 106f World-volume, 222
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Yang-Mills theory, 231, 257, 259 261
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z plane, mapping world sheet of closed string to, 106f Zero-dimensional objects, 28 29 Zero modes of ghost states, 124 Zeroth law, 246 Zeroth mode, 233
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