Gravity and Strings

isotropic, 198, 216, 232, 234, 265, 271, 532–535
Kruskal–Szekeres (KS), 192–193, 194, 209–211
Schwarzschild, see Schwarzschild, coordinates
spherical, 634
correspondence principle, 245, 577, 578, 589
cosmological constant, 102–103
cotangent space, 3
Coulomb
field, 200, 233
force, 218
covariant derivative
of world-tensor densities, 6
of world tensors, 5
of Yang–Mills fields, see Yang–Mills, covariant derivative
crosscaps, 412
CSK, see Cartan–Sciama–Kibble (CSK) theory
curvature, see tensor, curvature
curve, 7
Curzon, see solution, Chazy–Curzon
Dp-brane
solution, see solution, Dp
Dp-branes
defined, 420
D-instanton, see solution, D(−1)
de Broglie wavelength, 52
De Donder gauge, 57, 65, 65, 87, 282
de Sitter (anti-)
N = 1, d = 4 superalgebra, 152
gauging, 152–155
N = 1, d = 4 supergravity, 151, 159–160, 377
action, 154, 159
supersymmetry transformations, 160, 168
vacua, 384–386
N = 2, d = 4 supergravity, 151, 167–169, 378, 382
action, 168
solutions, 400
vacua, 389–390
N = 4, d = 5 (SO(6)-gauged) supergravity, 540, 563
N = 4, d = 7 (SO(5)-gauged) supergravity, 536
N = 8, d = 4 (SO(8)-gauged) supergravity, 534
(gauged) supergravities from spontaneous compactification, 547
algebra, 143, 385
spinorial representations, 629–633
connection, 167
group, 46, 115, 132, 142, 143, 150, 159
gauging of, 143
radius, 143
spacetime, 103, 104, 143, 159, 161, 179, 235, 286, 372
stability, 372
superalgebras, 563
supergroup, 150
Dehn twists, 336
Demiański
Plebański–Demiański solutions, see solution, Plebański
Deser, 45, 176
Abbott–Deser approach, see Abbott–Deser approach
argument for GR’s self-consistency, 44, 46, 59, 78, 85, 89–93
Boulware–Deser paper, see Boulware
diamond invariant of E 7, 587, 588
Dicke, see Jordan–Brans–Dicke theory
differential form, 3,6,23
dilaton a-model, 350–358, 515
and secondary hair, 216
equations of motion, 351
dilaton BHs, 574
dilaton field, 121, 149, 216, 218, 303, 307, 313, 412, 420, 426,
430–432, 439, 440, 445, 447, 453, 455–457, 464, 471, 477,
480, 498, 510, 515, 530, 537, 569, 571, 576, 580
and electric–magnetic duality, 516
and fundamental p-brane frames, 510
and S duality, 490
Index 673
and the string coupling constant, 425, 487
Buscher’s T-duality transformation rule, 438
coupling to D-branes, 511
coupling to fundamental branes, 511
coupling to Kaluza–Klein (KK) branes, 512
coupling to solitonic branes, 511
coupling to the Dp-brane, 434
coupling to the string, 433
dimensional reduction on S 1 , 436, 549
dimensional reduction on T p , 550
from N = 1, d = 11 supergravity, 457–458, 470, 475
Dirac
conjugate, 18, 152, 468, 601, 615, 621
and Majorana spinors, 617
in arbitrary signature, 628
conjugation matrix, 601, 613, 615, 621
in arbitrary signature, 627
delta function, 69, 71, 234, 518, 519
equation, 415, 614, 617
conjugate, 615, 616
from superparticle action, 412, 413
magnetic monopole, 248–254, 276
and SU(2)/U(1) coset space, 608
and Hopf fibrations, 636
and Wu–Yang formulation, 255
equation, 249, 249, 272, 277, 328
no existence for gauge group R, 253
solution, 250, 252
magnetic monopoles
absence in massive electrodynamics, 226
massive equation
from superparticle action, 413
matrices, see gamma matrices
quantization condition, 254, 254
and Aharonov–Bohm phase, 254
and the time periodicity of the Taub–NUT solution, 270
and Wu–Yang formulation, 255
for extended objects, 500
for extended objects, 508, 509, 520, 550
for extended objects and the Newton constant, 528, 529
in Kaluza–Klein (KK) theories, 306, 312, 329, 339
spinor, 612
and Wilson lines, 347
commuting in WNI technique, 181
energy–momentum tensor, 36, 37, 39
energy–momentum tensor coupled to gravity, 130, 131
energy–momentum tensor coupled to gravity in first-order
formalism, 139–140
Lorentz transformations, 614
reducible in even d, 616
string singularities
and the wire singularities of the Taub–NUT solution, 270
string singularity, 251–255
for extended objects, 508
Dirac–Schwinger–Zwanziger (DSZ) quantization condition, 214,
256
and S duality, 362
and S duality, 258
Dirichlet (D) boundary conditions, 411
divergence
modified, 8
Dreibein, 14
DSZ, see Dirac–Schwinger–Zwanziger (DSZ) quantization
condition
Eckart–Schrödinger representation, 600
Eguchi, see solution, Eguchi–Hanson
Einbein, 14
Einstein, 69, 73, 95, 99, 102
and the gravity energy–momentum tensor, 171
equation
in axion–dilaton gravity, 361