Index
419
gauge field A μ , 8
gauge invariance, 9
momentum expansion, 9
tachyon T , 8
Operator product expansion, 122
GG, 340
T -primary, 124
T G, 340
T T , 124
identity-primary, 123
Out-of-Siegel gauge constraint, 219
P
p-brane, 1
P 1 , 44, 46
ˆ
P g,n , 254
P g,n space, 247
p-form, 269, 271
BRST identity, 278
properties, 275–279
0-form, 270
1-form, 270–271
coordinates, 255
section, 247, 294
vector, 255–257
P g,m,n space, 346
p-form, 346
1-form, 347
Path integral
Faddeev–Popov gauge fixing, 39
field redefinition, 395
measure, 36, 394
free-field, 36, 395
ultralocality, 36, 56
Picture changing operator, 355
Picture number, 341
anomaly, 342, 346
Plumbing fixture, 257, 258, 285, 348
p-form, 287
ghost 1-form, 286
moduli, 258
non-separating, 261–262, 291
separating, 257–261, 286, 304
vector field, 286
Polyakov path integral, 29
complex representation, 96
Faddeev–Popov gauge fixing, 39, 73
Primary operator/state, 114
finite transformation, 115
weight-0, 119
Projector
on-shell, ker L 0 , 190
Propagator, 188, 189
closed bosonic, 290, 296–298
with stub, 303
closed string, 239–240
NS sector, 348
open bosonic, 217
R sector, 348
Schwinger parametrization, 15, 296
superstring, 354
Propagator region, 263
Punctured Riemann surface, 245
Euler characteristics, 245
parametrization, 251–252
Q
Quadratic differential, 46
Quasi-primary operator/state, 114
R
Radial quantization, 119
Reparametrization bc ghosts, 59
action, 59, 98
central charge, 54
equation of motion, 60
zero-mode, 62, 85
Riemann sphere S 2 , 105
complex plane map, 105
cylinder map, 108
Riemann surface
degeneration, 16
genus, 29
puncture, 13, 69
S
Scalar field CFT
L 0 , 155
U(1) current, 145, 147
U(1) symmetry, 145
action, 143, 146
boundary condition
periodic, 154
BPZ conjugate
modes, 159
vacuum, 159
central charge, 149
commutator, 156
complex components, 146
complex plane, 146
cylinder, 148
dual position, 153
energy–momentum tensor, 143, 147
equation of motion, 144, 146
419
gauge field A μ , 8
gauge invariance, 9
momentum expansion, 9
tachyon T , 8
Operator product expansion, 122
GG, 340
T -primary, 124
T G, 340
T T , 124
identity-primary, 123
Out-of-Siegel gauge constraint, 219
P
p-brane, 1
P 1 , 44, 46
ˆ
P g,n , 254
P g,n space, 247
p-form, 269, 271
BRST identity, 278
properties, 275–279
0-form, 270
1-form, 270–271
coordinates, 255
section, 247, 294
vector, 255–257
P g,m,n space, 346
p-form, 346
1-form, 347
Path integral
Faddeev–Popov gauge fixing, 39
field redefinition, 395
measure, 36, 394
free-field, 36, 395
ultralocality, 36, 56
Picture changing operator, 355
Picture number, 341
anomaly, 342, 346
Plumbing fixture, 257, 258, 285, 348
p-form, 287
ghost 1-form, 286
moduli, 258
non-separating, 261–262, 291
separating, 257–261, 286, 304
vector field, 286
Polyakov path integral, 29
complex representation, 96
Faddeev–Popov gauge fixing, 39, 73
Primary operator/state, 114
finite transformation, 115
weight-0, 119
Projector
on-shell, ker L 0 , 190
Propagator, 188, 189
closed bosonic, 290, 296–298
with stub, 303
closed string, 239–240
NS sector, 348
open bosonic, 217
R sector, 348
Schwinger parametrization, 15, 296
superstring, 354
Propagator region, 263
Punctured Riemann surface, 245
Euler characteristics, 245
parametrization, 251–252
Q
Quadratic differential, 46
Quasi-primary operator/state, 114
R
Radial quantization, 119
Reparametrization bc ghosts, 59
action, 59, 98
central charge, 54
equation of motion, 60
zero-mode, 62, 85
Riemann sphere S 2 , 105
complex plane map, 105
cylinder map, 108
Riemann surface
degeneration, 16
genus, 29
puncture, 13, 69
S
Scalar field CFT
L 0 , 155
U(1) current, 145, 147
U(1) symmetry, 145
action, 143, 146
boundary condition
periodic, 154
BPZ conjugate
modes, 159
vacuum, 159
central charge, 149
commutator, 156
complex components, 146
complex plane, 146
cylinder, 148
dual position, 153
energy–momentum tensor, 143, 147
equation of motion, 144, 146