Index
417
Dual state, see Conjugate state
E
(scalar action sign), 143
ηξ ghosts, 341
Energy–momentum tensor
finite transformation, 124
mode expansion, 129
Energy vacuum, 131
Euclidean adjoint, 125–126
mode, 128
state, 132
Euler characteristics, 30, 70
Extended complex plane ¯
C, 105
F
Factorization, see String amplitude
Faddeev–Popov
determinant, 50
gauge fixing (see Path integral)
Field space
DeWitt metric, 37
inner-product, 36, 393
norm, 36, 393
See also Path integral
Field theory space, 329
connection, 330
Hilbert space bundle, 330
First-order CFT, 160
L 0 , 167, 173
U(1) ghost current, 162, 173
mode expansion, 167
transformation law, 164
U(1) symmetry, 160, 162
action, 160, 161
boundary condition, 166
BPZ conjugate
modes, 178
vacuum, 178
central charge, 163
commutator, 168
complex components, 160
cylinder, 164
energy–momentum tensor, 161
mode expansion, 167
energy normal ordering, 173
equation of motion, 161
Euclidean adjoint
modes, 177
vacuum, 178
Fock space, 176 (see also Hilbert space)
ghost charge, 163
ghost number, 162, 173
cylinder, 164
Hilbert space
full, 176
holomorphic, 176
inner product, 178
level operator, 167
mode expansion, 166
number operator, 166
OPE, 163–166
propagator, 162
summary, 179
vacuum
SL(2, C), 170
conjugate, 179
energy, 170–172
Virasoro operators, 167, 173
weight, 161
zero-mode decomposition, 176
zero-point energy, 171
Free covariant SFT
closed bosonic, 231
action, 318
classical action, 231
equation of motion, 230
gauge fixed action, 232, 313
gauge fixed equation of motion, 218,
232, 316
gauge transformation, 232
open bosonic
BV action, 225
classical action, 213, 215
equation of motion, 213
gauge fixed action, 218
gauge transformation, 216, 226
zero-mode decomposition, 215
Free SFT, 190
Free super-SFT
action, 355–357
gauge transformation, 355–357
Fundamental vertex
interpretation, 316
region, 263
G
Ghost number, 60
anomaly, 279, 346
Gluing compatibility, 261
Green function, 71–73, 295
tree-level 2-point, 302
Group
fundamental domain, 42
volume, 41
417
Dual state, see Conjugate state
E
(scalar action sign), 143
ηξ ghosts, 341
Energy–momentum tensor
finite transformation, 124
mode expansion, 129
Energy vacuum, 131
Euclidean adjoint, 125–126
mode, 128
state, 132
Euler characteristics, 30, 70
Extended complex plane ¯
C, 105
F
Factorization, see String amplitude
Faddeev–Popov
determinant, 50
gauge fixing (see Path integral)
Field space
DeWitt metric, 37
inner-product, 36, 393
norm, 36, 393
See also Path integral
Field theory space, 329
connection, 330
Hilbert space bundle, 330
First-order CFT, 160
L 0 , 167, 173
U(1) ghost current, 162, 173
mode expansion, 167
transformation law, 164
U(1) symmetry, 160, 162
action, 160, 161
boundary condition, 166
BPZ conjugate
modes, 178
vacuum, 178
central charge, 163
commutator, 168
complex components, 160
cylinder, 164
energy–momentum tensor, 161
mode expansion, 167
energy normal ordering, 173
equation of motion, 161
Euclidean adjoint
modes, 177
vacuum, 178
Fock space, 176 (see also Hilbert space)
ghost charge, 163
ghost number, 162, 173
cylinder, 164
Hilbert space
full, 176
holomorphic, 176
inner product, 178
level operator, 167
mode expansion, 166
number operator, 166
OPE, 163–166
propagator, 162
summary, 179
vacuum
SL(2, C), 170
conjugate, 179
energy, 170–172
Virasoro operators, 167, 173
weight, 161
zero-mode decomposition, 176
zero-point energy, 171
Free covariant SFT
closed bosonic, 231
action, 318
classical action, 231
equation of motion, 230
gauge fixed action, 232, 313
gauge fixed equation of motion, 218,
232, 316
gauge transformation, 232
open bosonic
BV action, 225
classical action, 213, 215
equation of motion, 213
gauge fixed action, 218
gauge transformation, 216, 226
zero-mode decomposition, 215
Free SFT, 190
Free super-SFT
action, 355–357
gauge transformation, 355–357
Fundamental vertex
interpretation, 316
region, 263
G
Ghost number, 60
anomaly, 279, 346
Gluing compatibility, 261
Green function, 71–73, 295
tree-level 2-point, 302
Group
fundamental domain, 42
volume, 41