Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Index More information Index acceleration equation, 528 multiloop, 91 action off-shell, 105 p-brane, 7, 19, 23 one-loop, 94 sigma-model form, 29 Shapiro–Virasoro, 91 D0-brane, 149, 185 anomalous dimension, 653, 672 Einstein–Hilbert, 301 BMN operator, 680 in D dimensions, 550 anomaly Einstein–Maxwell, 560 characteristic class, 174, 176, 177 Nambu–Goto, 24, 26, 27, 155 conformal, 62, 66, 76, 658 point-particle, 18 form, 174, 178 nonrelativistic limit, 20 hexagon diagram, 170 Polyakov, 26 inflow mechanism, 183 string sigma-model, 26, 30, 37 M5-brane, 184 cosmological constant term, 28 NS5-brane, 184 supergravity in 11 dimensions, 304 R symmetry, 657, 673, 676 type I supergravity, 318 superconformal, 143 type IIA supergravity, 311 triangle diagram, 170 type IIB supergravity, 314, 317 anomaly cancellation, 9, 421 ADE E8 × E8,179 classification of singularities, 360, 436 SO(16) × SO(16), 292 Dynkin diagrams, 423 11-dimensional supergravity, 181 gauge group, 437 at M-theory boundary, 182 groups, 422, 423 heterotic M-theory, 470 subgroups of SU(2), 437 in six dimensions, 182, 426, 454 adjunction formula, 370 R symmetry, 672 Adler–Bardeen theorem, 170 type I superstring theory, 176 AdS/CFT duality, 15, 330, 612, 638 type IIB superstring theory, 175 for D3-branes, 638, 642 anthropic principle, 522 for half-BPS states, 654 anthropic reasoning, 15, 522 for M2-branes, 643 anti-de Sitter space, 15, 375, 377, 612 for M5-branes, 644 D = 4, 351 affine connection, 445 D = 5, 494 affine Lie algebra, 68 boundary-operator renormalization, 653 Aharanov–Bohm effect, 198 conformal equivalence class, 652 Aichelburg–Sexl metric, 633 covering space, 646 almost complex structure, 448, 466 Euclideanized, 647, 651 amplitude Feynman rules, 652 N tachyon, 91 global coordinates, 647, 686 absence of UV divergence, 83 in (d + 1) dimensions, 616 D0-brane scattering, 630 nonnormalizable modes, 654 in GS formalism, 148 normalizable modes, 654 large-N gauge-theory, 641 path integral, 651 M-theory, 632 Penrose diagram, 646 726 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Index More information Index 727 Poincar´e coordinates, 645, 646, 686 extremal for D =5,559 antibrane, 211 temperature of, 565 anticommutation relations rotating and BPS for D = 5, 573 fermionic oscillators, 124, 164 Schwarzschild, 552, 554 heterotic string fermions, 256 in D dimensions, 553 world-sheet fermion fields, 120 supermassive, 549 area law, 661, 662 temperature of, 562 attractor equation, 590, 593 thermodynamic properties, 14, 562 attractor mechanism, 587 black ring, 596, 608 auxiliary field blow-up, 367, 368, 373, 435, 455 in point-particle action, 19, 22, 145, 185 BMN limit, 680 in world-sheet supermultiplet, 113–115 BMN operator, 680 PST, 314 anomalous dimension, 680 world-sheet metric, 7, 26, 27, 31 correlation function, 681 axion, 316, 401, 492, 498, 541 Born–Infeld action, 231, 246, 687 axion–dilaton field, 316, 476, 481, 484, 485, bosonic ghost fields, 142 524 bosonic string, 17 number operator, 43 background fields, 81, 89, 227, 228, 230, 237, bosonization, 67 267, 275, 281, 295, 628, 629 of ghosts, 80 NS–NS, 227, 237, 245 bound state R–R, 229, 237 of D0-branes, 331, 626 background-field gauge condition, 627 of strings, 328 Bekenstein–Hawking entropy formula, 14, 563, threshold, 331 603, 609, 648 boundary condition leading correction to, 585 Dirichlet, 33, 164, 187, 193–195, 201, 202, Beltrami differential, 92 210, 622, 623 Bertotti–Robinson metric, 562 Neumann, 164, 202, 209 Betti numbers, 363, 442 boundary state, 171 SN of , 443 BPS Bianchi identity (p, q) string, 327 for antisymmetric tensor field, 245 bound, 151, 297, 300, 353, 408, 485, 655 for four-form in heterotic M-theory, 521 D-string, 325 for Maxwell field, 560 branes, 296, 421 for Riemann tensor, 384 tensions, 307, 341 with H flux, 511, 516 D-branes, 208, 209, 213, 228, 230, 621, 638 with D3-brane source, 483, 492 type IIA, 405 with M5-brane source, 353 Big Bang, 16 type IIB, 328, 405 biholomorphic function, 61 F-string, 221 Birkhoff’s theorem, 552 M-branes, 307, 332, 614 black p-branes, 14, 551, 613 M-theory solutions, 617 nonextremal, 625 states, 298, 328, 408 black D-branes in nine dimensions, 340 nonextremal, 686 wrapped D-branes, 414 black holes, 14, 408, 549 tensions, 427 challenges posed by, 550 brane–antibrane annihilation, 212, 587 dyonic, 590 brane–antibrane inflation, 537, 540 entropy of, 14, 563, 570, 604 brane–brane inflation, 539 extremal, 558 brane-world scenario, 11, 354, 459, 493 with four charges for D = 4, 574 Brink–Schwarz superparticle, 185 with three charges for D = 5, 567 BRST inner and outer horizons, 557 charge, 77 multi-center solutions, 594 for RNS string, 143 nonextremal, 572 mode expansion, 77 D = 4, 581 nilpotency, 78, 107 D = 5, 586 cohomology, 79, 108 production at accelerators, 552 quantization, 75, 108 Reissner–Nordstr¨om, 557 symmetry, 77 entropy of, 564 of RNS string, 142 extremal, 558 bubbling AdS, 655 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Index More information 728 Index Calabi–Yau four-fold, 458, 460–463, 466, 467, chiral fields, 170, 174 469, 471, 477, 478, 547, 548 of type I theory, 176 elliptically fibered, 475 of type IIB theory, 175 examples, 476 on an M5-brane, 184 Hodge numbers, 473 self-dual tensor, 172, 175 holomorphich four-form, 474 Weyl fermion, 174 K¨ahler form, 473 Weyl gravitino, 175 Calabi–Yau manifold, 5, 10, 356 chiral matter, 417 n-folds, 363 chiral primary operator, 656, 672 mirror symmetry, 10 chiral superfield, 666 one-folds, 366 chiral supermultiplet, 417, 473 two-folds, 366 chiral-symmetry breaking, 611 Calabi–Yau three-fold, 588 chirality, 134, 302 conifold singularity, 488 in ten dimensions, 136 elliptic fibration, 455 of dilatino, 137 Euler characteristic, 365 of gravitino, 137 heterotic string compactification, 415 of R sector, 136 Hodge diamond, 364 of type IIB theory, 136 intersection numbers of Weyl spinor, 134 of three-cycles, 392 projection operators, 134 K¨ahler form, 381 Christoffel connection, 23, 384, 509, 510, 513, M-theory compactification, 401, 410 517, 547 metric deformations, 388 Clifford algebra, 110, 166, 299 product structure of moduli space, 391 closed form, 442 quintic, 370 closed string, 32 supersymmetric three-cycle, 409 closed time-like curve, 359, 551, 645 special Lagrangian submanifold, 405 CMB anisotropy, 531 three-torus fibration, 414 cocycle, 67 type IIA compactification, 400, 402 cohomology, 79, 441 type IIB compactification, 400, 402, 403, BRST, 79, 87, 105, 108, 144 408, 588 classes, 79, 211, 321, 395, 589 volume form, 384 constraint, 416 calibration, 435, 439 de Rham, 442, 467 canonical homology basis, 590 canonical momentum, 35 Dolbeault, 449 Cartan matrix of Calabi–Yau four-fold, 474, 500 of Calabi–Yau three-fold, 392 E8, 294 SU(3), 285 of K3, 419 Casimir invariants of Riemann surface, 95 of SU(N), 657, 669 primitive, 467–469 central charge, 42, 62, 297, 300 cold dark matter, 531 central extension, 42, 57, 62 commutation relations, 55 Chan–Paton Kac–Moody algebra, 69 charges, 101, 196, 197, 222, 244, 250 of bosonic oscillators, 124 factors, 196 Poincar´e algebra, 56 index, 197 compactification, 5 matrix, 197, 198 F-theory chaotic inflation, 534 on K3, 427, 433 characteristic class, 157, 172–174 heterotic string factorization, 180 on a Calabi–Yau three-fold, 357, 374, 387, charge-conjugation matrix, 153 415, 418 Chern character, 174 on a three-torus, 420 factorization property, 177 with flux, 508 Chern class, 471 M-theory first, 363, 370, 371, 382, 451, 453 on a G2 manifold, 433, 434, 436 second, 186 on a Spin(7) manifold, 438 Chern–Simons form, 157, 174, 179, 186 on a Calabi–Yau four-fold, 461, 499 Chern–Simons term on a Calabi–Yau three-fold, 401, 405, 410 D7-brane, 483 on K3, 419, 423 in five dimensions, 658 with conical singularity, 436 chiral algebra, 71 on a circle, 188, 190, 193, 198, 199, 202, 209, © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Index More information Index 729 211, 214, 234, 244, 271, 329, 330, 333, infinitesimal, 61, 74 337, 339 special, 60, 62 toroidal, 265, 266, 268, 270, 274, 275, 278, conical singularity, 360, 670 280, 287, 288, 291, 340, 345, 397 conifold, 354, 487–489, 669, 671, 675, 684, 687 type IIA superstring deformed, 488, 490, 496, 498, 673, 675, 684 on a Calabi–Yau three-fold, 400, 402 with wrapped D6-branes, 685 on K3, 424–426 geometry, 489, 491 type IIB superstring isometry group, 489 on a Calabi–Yau three-fold, 400, 402, 403, K¨ahler form, 548 408, 498, 502 resolved, 488, 490, 684 on K3, 426, 454 with wrapped D5-branes, 685 with flux, 480 singularity, 403, 404, 454, 487, 488, 490, 497 warped, 355, 456 transition, 357, 385, 403, 487, 685 with branes, 376 warped, 492, 674 with flux, 13, 458 with fluxes, 491 complex geometry, 449 coordinate singularity, 554, 559 complex projective space, 369, 453 correlation functions, 73 Fubini–Study metric, 369 generating function, 652 K¨ahler potential, 369 coset-space theory, 69 complex structure, 90, 448, 513 cosmic censorship conjecture, 550, 551, 558 deformations, 370, 388, 391 cosmic