String Theory and M-Theory

728 Index
Calabi–Yau four-fold, 458, 460–463, 466, 467,
469, 471, 477, 478, 547, 548
elliptically fibered, 475
examples, 476
Hodge numbers, 473
holomorphich four-form, 474
Kähler form, 473
Calabi–Yau manifold, 5, 10, 356
n-folds, 363
mirror symmetry, 10
one-folds, 366
two-folds, 366
Calabi–Yau three-fold, 588
conifold singularity, 488
elliptic fibration, 455
Euler characteristic, 365
heterotic string compactification, 415
Hodge diamond, 364
intersection numbers
of three-cycles, 392
Kähler form, 381
M-theory compactification, 401, 410
metric deformations, 388
product structure of moduli space, 391
quintic, 370
supersymmetric three-cycle, 409
special Lagrangian submanifold, 405
three-torus fibration, 414
type IIA compactification, 400, 402
type IIB compactification, 400, 402, 403,
408, 588
volume form, 384
calibration, 435, 439
canonical homology basis, 590
canonical momentum, 35
Cartan matrix
E8, 294
SU(3), 285
Casimir invariants
of SU(N), 657, 669
central charge, 42, 62, 297, 300
central extension, 42, 57, 62
Chan–Paton
charges, 101, 196, 197, 222, 244, 250
factors, 196
index, 197
matrix, 197, 198
chaotic inflation, 534
characteristic class, 157, 172–174
factorization, 180
charge-conjugation matrix, 153
Chern character, 174
factorization property, 177
Chern class, 471
first, 363, 370, 371, 382, 451, 453
second, 186
Chern–Simons form, 157, 174, 179, 186
Chern–Simons term
D7-brane, 483
in five dimensions, 658
chiral algebra, 71
chiral fields, 170, 174
of type I theory, 176
of type IIB theory, 175
on an M5-brane, 184
self-dual tensor, 172, 175
Weyl fermion, 174
Weyl gravitino, 175
chiral matter, 417
chiral primary operator, 656, 672
chiral superfield, 666
chiral supermultiplet, 417, 473
chiral-symmetry breaking, 611
chirality, 134, 302
in ten dimensions, 136
of dilatino, 137
of gravitino, 137
of R sector, 136
of type IIB theory, 136
of Weyl spinor, 134
projection operators, 134
Christoffel connection, 23, 384, 509, 510, 513,
517, 547
Clifford algebra, 110, 166, 299
closed form, 442
closed string, 32
closed time-like curve, 359, 551, 645
CMB anisotropy, 531
cocycle, 67
cohomology, 79, 441
BRST, 79, 87, 105, 108, 144
classes, 79, 211, 321, 395, 589
constraint, 416
de Rham, 442, 467
Dolbeault, 449
of Calabi–Yau four-fold, 474, 500
of Calabi–Yau three-fold, 392
of K3, 419
of Riemann surface, 95
primitive, 467–469
cold dark matter, 531
commutation relations, 55
Kac–Moody algebra, 69
of bosonic oscillators, 124
Poincaré algebra, 56
compactification, 5
F-theory
on K3, 427, 433
heterotic string
on a Calabi–Yau three-fold, 357, 374, 387,
415, 418
on a three-torus, 420
with flux, 508
M-theory
on a G2 manifold, 433, 434, 436
on a Spin(7) manifold, 438
on a Calabi–Yau four-fold, 461, 499
on a Calabi–Yau three-fold, 401, 405, 410
on K3, 419, 423
with conical singularity, 436
on a circle, 188, 190, 193, 198, 199, 202, 209,