String Theory Demystified

306 String Theory Demystifi ed
Symmetries, of Polyakov action (Cont.):
Poincaré transformations, 56–57
reparameterizations, 57–58
Weyl transformations, 58–59
Symmetry breaking, 17
T
Tachyons
D-brane decay and, 235–237
ground state of bosonic string theory, 81–82
GSO projection, 148
Taus, 17
Taylor expansion, 171–172
T-duality
for closed strings, 159–161
D-branes, 164–165
open strings and, 162–164
overview, 192–193
Temperature
of black holes, 247–248
ekpyrotic, 276
Tensors. See individual tensors by name
Thermodynamics, 246
T’Hooft, Gerard, 256
Three-dimensional branes, 16
Topology, 17
Torus surface, 37f
Total number operators, 77, 197
Trace, calculating for energy-momentum tensor, 52–53
Transformations
BRST, 121–125
conformal, 90, 98–100
Möbius, 102
Poincaré
conserved currents from, 63–66
overview, 56–57
scale, 91–92
special conformal, 99
supersymmetry, 132–133
Weyl, 58–59
Two-dimensional conformal group, 100–104
Two-component Majorana spinors, 130
Two-dimensional conformal fi eld theories, 90
Two-point function, 107
Type I string theory, 14, 191
Type II A string theory
defi ned, 15, 191
massless spectrum of different sectors, 203–204
NS sectors, 195–196, 198–200
overview, 201–202
R sectors, 195–198
spin fi eld, 200–201
Type II B string theory
defi ned, 15, 191
massless spectrum of different sectors, 203–204
NS sectors, 195–196, 198–200
overview, 203
R sectors, 195–198
spin fi eld, 200–201
U
Uncertainty principle, 4, 9
Unifi cation, 11–12
Unoriented strings, 188–189
Uppercase letters in coordinates, 22
V
Vacuum fi eld equations, 241
Vanishing Euler characteristic, 37
Vibration of strings, 14, 92–93
Virasoro algebra with central extension, 80, 104
Virasoro constraints, 78
Virasoro operators, 78, 80, 155–156
Virtual processes, 7
Visible branes, 273
Volume elements, 96
W
Warp factor, 274
Wave equation solutions, 43–44
Wave function, 4–5
Weak particle interactions, 8
Weyl spinors, 149
Weyl transformations, 58–59
Wick expansion, 107–110
Wick rotations, 93
Winding contribution, 47
Winding mode, 154
Winding number, 47, 154
Winding states, 154
Witten algebra, 104
World line for point particle, 13f
Worldsheet currents
conserved currents from Poincaré invariance, 63–66
energy-momentum tensor, 52–53
hamiltonian, 67
overview, 51
supersymmetry transformations on, 132–133
symmetries of Polyakov action
overview, 53–56
Poincaré transformations, 56–57
reparameterizations, 57–58
Weyl transformations, 58–59
transforming to fl at metric, 59–63
Worldsheet supersymmetry, 171–173
Worldsheet for closed strings, 13f, 29f, 106f
World-volume, 222
Y
Yang-Mills theory, 231, 257, 259–261
Z
z plane, mapping world sheet of closed string to, 106f
Zero-dimensional objects, 28–29
Zero modes of ghost states, 124
Zeroth law, 246
Zeroth mode, 233