416
Index
3-point, 235
4-point, 237, 274
Closed string fundamental vertex, 294
g-loop
0-point, 302
1-loop
0-point, 303
1-point, 302
properties, 305–306
recursive construction, 298
special vertices, 302–303
tree-level
0-point, 303
1-point, 303
2-point, 302, 318
3-point, 237
4-point, 241
Closed string product, 305
g = 0, n = 1, 315, 318
ghost number, 305
Closed string states
dilaton , 9
Kalb–Ramond B μν , 9
level-matching (see Level-matching
condition)
massless field, 9
metric G μν , 9
tachyon T , 8
physical, 200
zero-mode decomposition, 243
Closed string vertex
fundamental identity, 306
Commutator
[L m , L n ], 117
[L m , φ n ], 129
CFT, 120–121
Complex coordinates, 92, 106
cylinder, 108
Conformal
anomaly (see Weyl, anomaly)
dimension, 115
factor (see Liouville, field)
spin, 115
vacuum (see SL(2, C) vacuum)
weight, 114
Conformal algebra, 102
2d (see Witt algebra; Virasoro algebra)
Conformal field theory
classical, 110
cylinder, 138
definition, 114
finite transformation, 115
Conformal isometry group, 101
sphere (see SL(2, C))
See also Conformal Killing vector
Conformal Killing
equation, 49, 102
group volume, 52
vector, 49, 75, 102
Conformal structure, 32
Conjugate state, 133
Conserved charge, 130, 375, 382
CFT, 121
Conserved current, 375
CFT, 121
mode expansion, 129
Contracting homotopy operator, 188, 195
Contraction, 123
Conventions
complex coordinates, 374
ghost number, 174
spacetime momentum current, 145
Correlation function, 117
quasi-primary operator, 118
sphere 1-point (-), 118
sphere 2-point (-), 118
sphere 3-point (-), 118
Covariant SFT, See also classical (-); free (-),
quantum (-)
background independence, 328
closed bosonic
1PI action, 323
1PI gauge symmetry, 324
classical action, 318
classical equation of motion, 318
classical gauge algebra, 319
classical gauge transformation, 319
fields and antifields, 322
gauge fixed action, 315, 316
inner product, 230, 231
normalization, 316
quantum action, 321
quantum BV master equation, 321
open bosonic
inner product, 213
parameters, 316
renormalization, 316
Critical dimension, 5, 11, 54, 98, 183, 186
superstring, 340
Cross-ratio, 119
D
Degeneration limit, 262
Diffeomorphism, 31
group volume, 43, 48, 51
infinitesimal (-), 31
large (-), 31
Index
3-point, 235
4-point, 237, 274
Closed string fundamental vertex, 294
g-loop
0-point, 302
1-loop
0-point, 303
1-point, 302
properties, 305–306
recursive construction, 298
special vertices, 302–303
tree-level
0-point, 303
1-point, 303
2-point, 302, 318
3-point, 237
4-point, 241
Closed string product, 305
g = 0, n = 1, 315, 318
ghost number, 305
Closed string states
dilaton , 9
Kalb–Ramond B μν , 9
level-matching (see Level-matching
condition)
massless field, 9
metric G μν , 9
tachyon T , 8
physical, 200
zero-mode decomposition, 243
Closed string vertex
fundamental identity, 306
Commutator
[L m , L n ], 117
[L m , φ n ], 129
CFT, 120–121
Complex coordinates, 92, 106
cylinder, 108
Conformal
anomaly (see Weyl, anomaly)
dimension, 115
factor (see Liouville, field)
spin, 115
vacuum (see SL(2, C) vacuum)
weight, 114
Conformal algebra, 102
2d (see Witt algebra; Virasoro algebra)
Conformal field theory
classical, 110
cylinder, 138
definition, 114
finite transformation, 115
Conformal isometry group, 101
sphere (see SL(2, C))
See also Conformal Killing vector
Conformal Killing
equation, 49, 102
group volume, 52
vector, 49, 75, 102
Conformal structure, 32
Conjugate state, 133
Conserved charge, 130, 375, 382
CFT, 121
Conserved current, 375
CFT, 121
mode expansion, 129
Contracting homotopy operator, 188, 195
Contraction, 123
Conventions
complex coordinates, 374
ghost number, 174
spacetime momentum current, 145
Correlation function, 117
quasi-primary operator, 118
sphere 1-point (-), 118
sphere 2-point (-), 118
sphere 3-point (-), 118
Covariant SFT, See also classical (-); free (-),
quantum (-)
background independence, 328
closed bosonic
1PI action, 323
1PI gauge symmetry, 324
classical action, 318
classical equation of motion, 318
classical gauge algebra, 319
classical gauge transformation, 319
fields and antifields, 322
gauge fixed action, 315, 316
inner product, 230, 231
normalization, 316
quantum action, 321
quantum BV master equation, 321
open bosonic
inner product, 213
parameters, 316
renormalization, 316
Critical dimension, 5, 11, 54, 98, 183, 186
superstring, 340
Cross-ratio, 119
D
Degeneration limit, 262
Diffeomorphism, 31
group volume, 43, 48, 51
infinitesimal (-), 31
large (-), 31