418
Index
GSO symmetry, 342
H
Hermitian adjoint, 125
Higher-genus Riemann surface
conformal group, 115
Hilbert space
CFT, 130
Holomorphic factorization, 98, 347
Holomorphic/anti-holomorphic sectors, 108,
372
I
iε-prescription, 364
Index
amplitude, 294
Riemann surface, 266, 294
Inversion map, 114, 126
Isometry group, 102
K
Killing vector, 102
L
L ± , 129
L ∞ algebra, 320, 353
Left/right-moving sectors, 108, 372
Level-matching condition, 8, 86, 199, 231, 243,
254, 277, 280, 297, 312, 355
Light-cone coordinates, 108
Liouville
action, 53
central charge, 54
field, 33, 53
free-field measure, 44
theory, 115, 117, 366
Local coordinates, 16, 236, 246
constraints, 254, 261
global phase, 253, 276, 279
global rescaling, 268
reparametrization, 254, 276, 277
transition function, 252, 254, 255
Logarithmic CFT, 118
M
Marginal deformation
action, 329, 330
correlation function, 330
Metric
gauge
conformal (-), 33
conformally flat (-), 33, 91
flat (-), 33
gauge decomposition, 42–44, 47, 57
gauge fixing, 33, 40
uniformization gauge, 33
Mode expansion, 127
Hermiticity, 128
mode range, 127
Modular group, 31, 41
Moduli space, 14, 41
complex coordinates, 97
plumbing fixture decomposition, 261–266,
267
with punctures, 245
Momentum-space SFT
action, 362
consistency, 366
Feynman rules, 362
finiteness
infinite number of states, 304, 363
UV divergence, 304, 363
Green function, 364
interaction vertex, 363
properties, 361
string field expansion, 362
N
Non-locality, 2, 362
Normal ordering, 134
conformal (-), 134
energy (-), 134
mode relation, 137
O
Off-shell closed string amplitude, 247, 272
contribution from subspace, 272
tree-level
3-point, 236
4-point, 300
Off-shell string amplitude, 16, 244
conformal invariance, 237
Off-shell superstring amplitude, 346
consistency, 346, 349
factorization, 348–349
PCO insertions, 346
supermoduli space, 347
Old covariant quantization (OCQ), 199
On-shell condition, 8, 71, 87, 120, 189, 195,
198, 199
Open string states
Index
GSO symmetry, 342
H
Hermitian adjoint, 125
Higher-genus Riemann surface
conformal group, 115
Hilbert space
CFT, 130
Holomorphic factorization, 98, 347
Holomorphic/anti-holomorphic sectors, 108,
372
I
iε-prescription, 364
Index
amplitude, 294
Riemann surface, 266, 294
Inversion map, 114, 126
Isometry group, 102
K
Killing vector, 102
L
L ± , 129
L ∞ algebra, 320, 353
Left/right-moving sectors, 108, 372
Level-matching condition, 8, 86, 199, 231, 243,
254, 277, 280, 297, 312, 355
Light-cone coordinates, 108
Liouville
action, 53
central charge, 54
field, 33, 53
free-field measure, 44
theory, 115, 117, 366
Local coordinates, 16, 236, 246
constraints, 254, 261
global phase, 253, 276, 279
global rescaling, 268
reparametrization, 254, 276, 277
transition function, 252, 254, 255
Logarithmic CFT, 118
M
Marginal deformation
action, 329, 330
correlation function, 330
Metric
gauge
conformal (-), 33
conformally flat (-), 33, 91
flat (-), 33
gauge decomposition, 42–44, 47, 57
gauge fixing, 33, 40
uniformization gauge, 33
Mode expansion, 127
Hermiticity, 128
mode range, 127
Modular group, 31, 41
Moduli space, 14, 41
complex coordinates, 97
plumbing fixture decomposition, 261–266,
267
with punctures, 245
Momentum-space SFT
action, 362
consistency, 366
Feynman rules, 362
finiteness
infinite number of states, 304, 363
UV divergence, 304, 363
Green function, 364
interaction vertex, 363
properties, 361
string field expansion, 362
N
Non-locality, 2, 362
Normal ordering, 134
conformal (-), 134
energy (-), 134
mode relation, 137
O
Off-shell closed string amplitude, 247, 272
contribution from subspace, 272
tree-level
3-point, 236
4-point, 300
Off-shell string amplitude, 16, 244
conformal invariance, 237
Off-shell superstring amplitude, 346
consistency, 346, 349
factorization, 348–349
PCO insertions, 346
supermoduli space, 347
Old covariant quantization (OCQ), 199
On-shell condition, 8, 71, 87, 120, 189, 195,
198, 199
Open string states