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Polchinski J. — String theory (volume 1). An introduction to the bosonic string
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Íàçâàíèå: String theory (volume 1). An introduction to the bosonic stringÀâòîð: Polchinski J. Àííîòàöèÿ: The two volumes that comprise String Theory provide an up-to-date, comprehensive account of string theory. Volume 1 provides a thorough introduction to the bosonic string, based on the Polyakov path integral and conformal field theory. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory, the Polyakov path integral, and the covariant quantization of the string. The book then treats string interactions: the general formalism, and detailed treatments of the tree level and one loop amplitudes. Toroidal compactification and many important aspects of string physics, such as T-duality and D-branes are also covered, as are higher-order amplitudes, including an analysis of their finiteness and unitarity, and various nonperturbative ideas. The volume closes with an appendix giving a short course on path integral methods, followed by annotated references, and a detailed glossary.
ßçûê: Ðóáðèêà: Ôèçèêà /Êâàíòîâàÿ òåîðèÿ ïîëÿ /Òåîðèÿ ñòðóí /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1998Êîëè÷åñòâî ñòðàíèö: 402Äîáàâëåíà â êàòàëîã: 25.09.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Dilaton, coupling to open strings 196—198 Dilaton, coupling to orientifold plane 280 Dilaton, dimensional reduction 233—234 241 Dilaton, effect of T-duality on 248 Dilaton, field equation 111—112 246 Dilaton, linear see "Linear dilaton CFT" Dilaton, moduli space 254 Dilaton, propagator (field theory) 276 Dilaton, spacetime action 114—115 196—198 225 275—276 Dilaton, vertex operator 104—107 Dimensional reduction 235 249 Dirichlet boundary condition 31 266—270 281 Dirichlet boundary condition, T-dual to Neumann 266—270 Discrete gauge symmetry 260—261 277—278 Disk, conformal to semi-infinite cylinder 63—68 Disk, expectation values 174—175 178 Disk, Riemann surface 168 Disk, string amplitudes 178—189 196—198 204—205 Disk, string amplitudes with D-branes 270 274 281—282 Disk, tadpole 197—198 223—226 Disk, tadpole, cancellation with projective plane 229 Divergences from boundary of moduli space 196 296 305—306 Divergences, analytic continuation past 181 287 Divergences, cancellation for SO(8192) 228—229 Divergences, IR 181 223—225 306—310 Divergences, UV 2—7 218—220 Divergences, UV, absence in string theory 4—5 79 219 223—225 309—310 Divergences, zero mode 173 Doubling trick 57 63 66 178 Dual resonance model 348 Duality see "T-duality" "World-sheet Effective field theory 110 114 117 188—189 196—197 270—273 309 Einstein metric 115 194 275 Einstein's equation 112—113 222 Electroweak scale 222 Energy-momentum tensor 13 91 Energy-momentum tensor and derivative with respect to moduli 161 210—211 Energy-momentum tensor as constraint 121 Energy-momentum tensor, boundary condition 56—57 Energy-momentum tensor, choice of 49 95 303 Energy-momentum tensor, conformal transformation 47—49 Energy-momentum tensor, trace anomaly 92—97 Energy-momentum tensor, traceless and holomorphic 43—44 Energy-momentum tensor, vanishes for Chan — Paton states 185 Enhanced gauge symmetry 242—244 248 254 Epsilon prescription 182 287—288 305—306 Equivalence classes, BRST 128 Equivalence classes, gauge 84 87 Equivalence classes, OCQ 123 Equivalence principle 115 Euclidean adjoint 202—203 336 Euclidean continuation 82—83 170 210 335 Euler number 96 101 118 152 Euler number, in string action 83—84 112 179 203 Exact state (BRST) 128 Exceptional Lie algebras 192 expectation values 34 36 Expectation values, calculations 169—178 201—202 208—213 Exponential operator 40 46 Exterior derivative 128 Faddeev — Popov determinant 86—90 154—158 Faddeev — Popov determinant on disk 176 Faddeev — Popov determinant on sphere 176 Faddeev — Popov determinant on torus 212—213 216—217 Faddeev — Popov determinant shortcuts 179 218 Faddeev — Popov determinant sign 156 177 345 Faddeev — Popov ghosts 51—52 88—90 126 Faddeev — Popov ghosts, boundary condition 90 Faddeev — Popov ghosts, central charge 94 Faddeev — Popov ghosts, vacuum 61 141 Faddeev — Popov procedure, general 126 Feynman diagrams vs string graphs 3—5 101 Feynman diagrams, calculation of D-brane interaction 275—276 Feynman diagrams, calculation of Weyl anomaly 119 Feynman diagrams, decomposition of string amplitudes 297—306 Fiducial metric 85 Field strength, three-index 109 112 234—235 First-quantization 310 Fischler — Susskind mechanism 308—309 Fixed point, orbifold 256—258 Fixed point, orbifold, UV 4 Flat direction 246 262—263 272—273 Free energy 321—322 328 Free parameters, absence of 6 83—84 112—113 Free scalar CFT 32—41 Free scalar CFT, expectation values 169—76 208—211 229 Free scalar CFT, left-, right-moving 238 Free scalar CFT, mode expansion 58—61 Free scalar CFT, state-operator mapping 63—65 Fuchsian group 292—293 Functional integral see "Path integral" Fundamental region 148—150 Fundamental region in torus amplitude 216 219—220 Gauge boson 1 4 Gauge boson, closed string 241—243 Gauge boson, closed string, amplitudes 242 Gauge boson, open string 28 123—124 135—136 Gauge boson, open string in BRST quantization 135—136 Gauge boson, open string in light-cone quantization 23 Gauge boson, open string in OCQ 123—124 Gauge boson, open string, amplitudes 187—189 205 Gauge boson, open string, vertex operator 107 Gauge coupling 115 234 242—245 276 Gauge interaction 2 28 78 184—192 Gauge transformation 107 Gauge-fixing see also "Specific gauges" Gauge-fixing dependence on gauge choice 90—91 121—122 126—128 Gauge-fixing, 17—18 25 84—86 131 154—155 Gauge-fixing, general 126—128 Gaussian-averaged gauges 127 General relativity 1—2 5 28 108 General relativity, off-shell amplitudes 104 Genus 100—101 150 Genus, large 315—317 Geodesic curvature 30 82 96 Geodesic distance 102 Geodesic equation 108 Ghost number 51 62 127 Ghost number, anomaly 119 158—159 177 Ghost number, of string field 313—314 Ghost number, states vs operators 65—66 Ghosts see "Faddeev — Popov ghosts" Global symmetry 189 Goldstone boson 233 Graded Lie algebra 143 Grand unification 2 5 Grassmann variables 35 88 156—158 341—345 Gravitational coupling, 114 Gravitational coupling, relation to gauge coupling 234 244—245 Gravitational coupling, relation to string coupling 194 205 Graviton in BRST quantization 137 Graviton in light-cone quantization 27 29—30 Graviton in OCQ 125 Graviton, coupling to D-brane 270—277 Graviton, coupling to open strings 196—198 Graviton, coupling to orientifold plane 280 Graviton, propagator (field theory) 276 Graviton, vertex operator 104—107 Gravity 1—7 78 Green's function 169—171 174—176 208 229—230 275 Hagedorn temperature 321—322 352 Hamiltonian and path integral 329—332 335—336 343 Hamiltonian, effect of backgrounds 250 264 Hamiltonian, in partition function 209 212—213 Hamiltonian, point particle 17 130 218 Hamiltonian, string 19—21 25—26 Hamiltonian, string, relation to 54 73 125 Handle 83 100—101 290—292 Handle, degenerating 97—98 101 224—226 229 295—296 305—309 Hard scattering 183—184 194 281—282 317—319 352 Heterotic string 348 Hidden sector 6 Higgs field 1 222 245—246 high temperature 320—322 High-energy scattering see "Hard scattering" "Regge Highest weight state 70—72 122 125 143 Highest weight state, and tensor (primary) operators 71 Holomorphic current 42 Holomorphic field 34 56 72 Holomorphic quadratic differential 152 Holomorphic transition functions 153—154 Holomorphic vector field 152 Hyperelliptic surface 294 Infrared (IR) divergences 181 223—225 306—310 Inheritance principle 258 261 Inner product, bilinear (Zamolodchikov) 199—204 Inner product, bilinear (Zamolodchikov), in sewing 301—302 Inner product, bilinear (Zamolodchikov), relation to Hermitean 202—204 Inner product, Fermi oscillator 343 Inner product, Hermitean 134—135 Inner product, positive 71—72 116—117 138 Inner product, traceless symmetric tensor 118 instantons 316 Interaction, irrelevant 3 Interaction, string 77—82 104 178ff Jacobi identity 128 133 143 Jacobi's abstruse identity 215 Jacobian, Berezin integral 345 Kac — Moody algebra 243 Kaluza — Klein gauge field 2 232—234 241—243 249 257 351 Kaluza — Klein states 232 245 Klein bottle, Riemann surface 207 Klein bottle, string amplitude 226—229 230 278 280 Large order behavior 315—317 Lattice, even self-dual 252—253 281 Lattice, momentum 251—253 281 Laurent expansion see "Mode expansion" Length, minimum 248 318 Level, current algebra 243—244 Level, oscillator 23 26—27 Level-matching 27 258 Light-cone coordinates 16 Light-cone gauge 17 Light-cone gauge, off-shell 104 Light-cone quantization, point particle 17 Light-cone quantization, string 17—30 349 Light-cone quantization, string, equivalence to BRST and OCQ 137—143 Linear dilaton theory 49—50 61 75 204 213 349 Linear dilaton theory, as background 113 120 323—324 328 Liouville field theory 325 Loop expansion 115 Lorentz invariance 12 106—107 116—117 290 Lorentz invariance in light-cone gauge 20—24 90 94 349 Mandelstam variables 180 Manifold, complex 153 Manifold, differentiable 153 Manifold, Riemannian 153 Mass-shell condition from vertex operators 101 106 Mass-shell condition in BRST 131 134 137—138 Mass-shell condition in light-cone quantization 17 22 26 Matrix elements, relation to path integral 199—201 332—334 Matrix models 326—327 352 Measure on moduli space 154—165 see Measure on moduli space, BRST invariance 160—161 Measure on moduli space, derivation 154—157 Measure on moduli space, gauge invariance 159—160 Measure on moduli space, gauge invariance in terms of determinants 157—158 Measure on moduli space, gauge invariance in terms of transition functions 161—164 Metric (spacetime) 9 108—118 Metric (spacetime), dimensional reduction 231—233 Metric (spacetime), Einstein 115 194 275 Metric (spacetime), internal 249ff Metric (spacetime), light-cone coordinates 16 Metric (spacetime), sigma model 115 Metric (spacetime), string 115 Metric (world-line) 10 Metric (world-line), gauge-fixing 129 145—146 Metric (world-sheet), constant curvature 292 Metric (world-sheet), flat 32—33 Metric (world-sheet), gauge-fixing 17 84—86 146—152 Metric (world-sheet), induced 11 15 Metric (world-sheet), minimal area 300 351 Metric (world-sheet), noncritical string 94—95 325—326 Metric (world-sheet), Polyakov 12—13ff Mnemonics, zero-point 73—74 125 Mode (or Laurent) expansion, 53 70 Mode (or Laurent) expansion, bc CFT 61 Mode (or Laurent) expansion, free scalar 26 58 Mode (or Laurent) expansion, free scalar 235—238 Mode (or Laurent) expansion, free scalar 257 Mode (or Laurent) expansion, holomorphic operator 56 Mode (or Laurent) expansion, open strings 20 57 62—63 Mode (or Laurent) expansion, open strings, Dirichlet 267 Model, solvable 323—327 Modular group 148—149 151 Modular group and theta functions 214—216 Modular group, spacetime 253—255 Modular group, surfaces without 207—208 223 278 Modular group, used to analyze asymptotics 213 224 227—228 Modular invariance 210 217—218 229—230 Modular invariance in orbifold compactification 257 259 Modular invariance in toroidal compactification 237 251—253 Modular invariance in twisting construction 260 Modular invariance, constraints from 213 304 350 Modular invariance, needed for consistency 220 Modular invariance, one-point function 304 Moduli (spacetime) 233—234 249 265 Moduli (spacetime), moduli space 253—255 Moduli (spacetime), moduli space, branches 262 Moduli (spacetime), moduli space, c=1 261—263 351 Moduli (spacetime), moduli space, metric on 254 Moduli (world-sheet), boundary of 161 295—296 300 Moduli (world-sheet), boundary of, asymptotics 302—303 Moduli (world-sheet), boundary of, divergences from 196 224—226 300 305—309 Moduli (world-sheet), encoded in transition functions 152—154 161—164 Moduli (world-sheet), for metric 147—152 Moduli (world-sheet), graphical decomposition 297—300 351 Moduli (world-sheet), in open string field theory 313—314 316—317 Moduli (world-sheet), measure on 154—165 350 Moduli (world-sheet), moduli space 148—152 290—294 Moduli (world-sheet), total derivative on 161 196 220 288 Moduli (world-sheet), vertex operator positions 150—151 163—164 Moebius group 56 167 Moebius strip, Riemann surface 208 Moebius strip, string amplitude 228—229 280 Moebius transformation 178—180 192 198—199 Nambu — Goto action 10—13 15 28 30 Narain compactification 251—255 351 Naturalness problem 2 Neumann boundary condition 14 31 62 174 Neumann boundary condition, T-dual to Dirichlet 265—270 Nilpotence see "BRST" No-ghost theorem 137—143 350 Noether's theorem 41—43 74—75 Noether's theorem, anomalous 159 Noether's theorem, as local property 86 Non-Abelian gauge theory 188—192 243 Non-Abelian gauge theory from string field theory 313 Non-Abelian gauge theory on D-brane 272—273 Noncommutative geometry 272 Noncritical string theory 325—327 Nonlinear sigma model 108—110 120 349 Nonperturbative effects 234 248 269 310 315—317 Nonperturbative effects, 317 327 Normal ordering, boundary 75 175 Normal ordering, conformal 36—40 50 60 Normal ordering, constants 22—23 27 76 Normal ordering, constants from state-operator mapping 72 Normal ordering, constants from Virasoro algebra 59 61 Normal ordering, constants, direct calculation 60
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