Gravity and Strings

extended, 121, 150, 160–163, 379, 381
quasi-central charges, 397
gauged, see de Sitter (anti-)
hidden symmetries and dualities, 448
manifest duality invariance in the Einstein frame, see Einstein,
frame, manifest duality invariance
massive, 342
Romans’, see Poincaré, N = 2A, d = 10 massive (Romans’)
supergravity
matter fields, 316
Poincaré, see Poincaré
rheonomic approach, 139
supersymmetric solutions, 396
and string states, 408
vacua, 374, 379
supergravity theory, 374
superparticle (Green–Schwarz), see Green–Schwarz
superpotential, 31
superstring (Green–Schwarz), see Green–Schwarz
supersymmetric states, see BPS states
surface gravity, 198, 212
and temperature, 204
and temperature in d dimensions, 212
of Schwarzschild solution, see solution, Schwarzschild, surface
gravity
Susskind, 206
S duality, 247, 262, 291, 338, 500, 586, 588
and generation of solutions, 329
group, 338
in N = 4, d = 4 supergravity, 361, 362, 363, 366, 401
in 4d axion-dilaton gravity, 359–361
in 4d dilaton a-model, 357–358
in 4d Kaluza–Klein (KK) theory, 310–313, 408
and generation of solutions, 328
in axion–dilaton gravity, 349
in string theory, 407, 407
invariance of the DSZ quantization condition, 258
of N = 2B, d = 10 supergravity
solutions, 555–556, 564
superalgebra, 558
of N = 2B, d = 10 supergravity and the type-IIB superstring,
488–491
of heterotic superstring theory on T 6 , 448, 480, 482
of type-IIB superstring theory, 447, 485, 494, 497, 521–522,
523–525, 539, 542, 549
and its relation to M theory on T 2 , 493
tadpoles, 424
tangent space, 3
Taub-bolt, see solution, Taub-bolt
Taub–NUT, see solution, Taub–NUT
Teitelboim, see solution, BTZ black hole
tensor, 3
angular momentum, see angular-momentum tensor
Bel–Robinson, see Bel–Robinson tensor
Belinfante, see energy–momentum tensor, Belinfante
curvature
of GL(d, R) connection, 16
of affine connection, see Riemann, tensor
of Yang–Mills fields, 597
density, 4
Einstein, see Einstein, tensor
energy–momentum, see energy–momentum tensor
Lovelock, see Lovelock tensor
non-metricity, 9
Ricci, see Ricci, tensor
spin–energy potential, see spin–energy potential
torsion, see torsion
Weyl, see Weyl, tensor
tentor, 146
tetrad, 14
Thirring, 46, 59, 70, 82, 87
Index 683
Thorne, 194
Tod, 399, 400
torsion, 6,8
modified, 8
Townsend, 188, 437
Nicolai–Townsend transformations, see Nicolai–Townsend
translation group, see Lie, group, translation
trator, 146
twisted sectors, 421
type-I superstring theories, see string, type II
type-I ′ superstring theory, see string, type I ′
type-II superstring theories, see string, type II
tyupkin, see solution, BPST instanton
T duality, 247, 426–588
and D-branes, 443–445
and O-planes, 424
and string BH solutions, 587
between E 8 × E 8 and SO(32) heterotic superstrings on S 1 , 478
between massive N = 2A, d = 10 and N = 2B, d = 10
supergravity, 466
between type-I and type-I ′ theories, 499
between type-IIA and type-IIB theories, 491, 522
and extended objects, 522–523, 524–526, 541
and intersections of extended objects, 565
and the Chern–Simons term, 451, 487
and the superalgebra, 559
Buscher’s rules, see Buscher T duality, in type-II theories
between winding and momentum modes, 441–442
Buscher’s rules, see Buscher T duality
group for the heterotic string on T n
and pure N = 4, d = 4 supergravity, 482
group for the heterotic superstring on T n , 448, 473, 477, 480
in N = 4, d = 4 supergravity, 361, 362, 363, 366, 401
selfdual radius and symmetry enhancement, 313
U duality, 247, 312, 407, 523, 578, 586
and string BH solutions, 587
diamond-invariant, 587
groups in various dimensions, 449
Vafa, see Strominger–Vafa paper
van Nieuwenhuizen, 164
vector, 3
world, 4
Vielbein, 11, 14
Ansatz for dimensional reduction from d = 11 to d = 10, 456
Ansatz for dimensional reduction on S 1 , 300
Ansatz for dimensional reduction on T n , 332
energy–momentum tensor, 128, 133, 135, 136
conservation, 129
for a Dirac spinor, 131
relation to the canonical energy–momentum tensor,
130, 134
first postulate, 16, 16, 17, 17, 18, 20
formalism, 19, 113
for the Einstein–Hilbert action, 136
second postulate, 16
Vierbein, 14
von der Heyde model, 148
Wald, 80, 203
Wallach, see Cahen–Wallach symmetric spacetimes
Weinberg, 59, 78
Weitzenböck
connection, 11, 19, 145
invariants, 145
spacetime, 11, 19–20, 145
and teleparallelism, 20, 145
Wess–Zumino (WZ) term
for p-branes, 528
for a point-particle, 224, 225, 306