420
Index
Euclidean adjoint
modes, 159
vacuum, 159
Fock space, 157
Hilbert space, 158
inner product, 159
level operator, 154
mode expansion, 6, 152–153, 154
momentum, 145, 147, 152, 154
normal ordering, 152
number operator, 154
OPE, 148–151
periodic boundary condition, 143
position (center of mass), 153
propagator, 144
topological current, 145, 147
vacuum, 157
conjugate, 159
vertex operator, 148
Virasoro operators, 155
winding number, 145, 147, 152, 154
zero-mode, 152–153
Scattering amplitude, 71–73
tree-level 2-point (-), 72
Schwarzian derivative, 124
Section of P g,n
generalized, 306
overlap, 307
Siegel gauge, 191, 217, 227, 232
SL(2, C) group, 112
SL(2, C) vacuum, 130
Spacetime ghost number
closed string, 310
open string, 220
Spacetime level-truncated action
open bosonic, 226
gauge transformation, 228
Spacetime momentum, 145
Spurious pole, 346, 349–353
State (CFT)
bra, 132
ket, 130
State–operator correspondence, 130
Stokes’ theorem, 95
String
gauge group, 11
interactions, 2, 12
orientation, 11
parameters, 13
properties, 5
String amplitude, 13
CKV gauge fixing, 75
conformal invariance, 235
divergence, 15
factorization, 239, 285, 293
ghost number, 279
g-loop n-point (-), 70, 76–78
g-loop vacuum (-), 35, 57, 60, 63, 64, 97
matching QFT, 71–72, 78
normalization, 65, 70
properties, 279–283
pure gauge states decoupling, 282
section independence, 281
tree-level 2-point (-), 78–82
String coupling constant, 13
String Feynman diagram, 237
1PR diagram, 289, 304
change of stub parameter, 304
Feynman rules, 293
intermediate states
ghost number, 291, 292
momentum, 291, 293
IR divergence, 316
loop diagram, 292
String field
closed bosonic, 230
classical, 318
expansion, 309, 321
quantum, 321
expansion, 208
functional, 205
ket representation, 206
momentum expansion, 19, 207, 362
open bosonic, 213
classical, 214
expansion, 219
Nakanishi–Lautrup auxiliary field, 227
parity, 214
quantum, 221
reality condition, 214
position representation, 206
String field path integral
Faddeev–Popov gauge fixing, 222
free covariant open bosonic string, 222
String field theory, 18
construction, 16
String states, 6, 241–244
dual, 242
off-shell, 241
resolution of identity, 242
String theory
background independence, 328
consistency, 78, 366
motivations, 1–4
Structure constant (CFT), 118
Stub, 266–268
Feynman diagram, 303–304
parameter, 266
Index
Euclidean adjoint
modes, 159
vacuum, 159
Fock space, 157
Hilbert space, 158
inner product, 159
level operator, 154
mode expansion, 6, 152–153, 154
momentum, 145, 147, 152, 154
normal ordering, 152
number operator, 154
OPE, 148–151
periodic boundary condition, 143
position (center of mass), 153
propagator, 144
topological current, 145, 147
vacuum, 157
conjugate, 159
vertex operator, 148
Virasoro operators, 155
winding number, 145, 147, 152, 154
zero-mode, 152–153
Scattering amplitude, 71–73
tree-level 2-point (-), 72
Schwarzian derivative, 124
Section of P g,n
generalized, 306
overlap, 307
Siegel gauge, 191, 217, 227, 232
SL(2, C) group, 112
SL(2, C) vacuum, 130
Spacetime ghost number
closed string, 310
open string, 220
Spacetime level-truncated action
open bosonic, 226
gauge transformation, 228
Spacetime momentum, 145
Spurious pole, 346, 349–353
State (CFT)
bra, 132
ket, 130
State–operator correspondence, 130
Stokes’ theorem, 95
String
gauge group, 11
interactions, 2, 12
orientation, 11
parameters, 13
properties, 5
String amplitude, 13
CKV gauge fixing, 75
conformal invariance, 235
divergence, 15
factorization, 239, 285, 293
ghost number, 279
g-loop n-point (-), 70, 76–78
g-loop vacuum (-), 35, 57, 60, 63, 64, 97
matching QFT, 71–72, 78
normalization, 65, 70
properties, 279–283
pure gauge states decoupling, 282
section independence, 281
tree-level 2-point (-), 78–82
String coupling constant, 13
String Feynman diagram, 237
1PR diagram, 289, 304
change of stub parameter, 304
Feynman rules, 293
intermediate states
ghost number, 291, 292
momentum, 291, 293
IR divergence, 316
loop diagram, 292
String field
closed bosonic, 230
classical, 318
expansion, 309, 321
quantum, 321
expansion, 208
functional, 205
ket representation, 206
momentum expansion, 19, 207, 362
open bosonic, 213
classical, 214
expansion, 219
Nakanishi–Lautrup auxiliary field, 227
parity, 214
quantum, 221
reality condition, 214
position representation, 206
String field path integral
Faddeev–Popov gauge fixing, 222
free covariant open bosonic string, 222
String field theory, 18
construction, 16
String states, 6, 241–244
dual, 242
off-shell, 241
resolution of identity, 242
String theory
background independence, 328
consistency, 78, 366
motivations, 1–4
Structure constant (CFT), 118
Stub, 266–268
Feynman diagram, 303–304
parameter, 266