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Gravity and Strings Tomás Ortín Index More Information Cambridge University Press 978-0-521-82475-0 - Gravity and Strings Tomás Ortín Index More information Index Page numbers in italic are those on which the definition or a very ic discussion of the subject can be found. 4d means four dimensions or four-dimensional, etc. AdSj, see anti-de Sitter (AdS) spacetime Ashtekar variables, 138 /?-brane asymptotically locally Euclidean (ALE) solutions, 272 (a\-a'i) model for intersecting branes, 570-573 Atiyah, see solution, Atiyah-Hitchin action, 570 autoparallel a-model, 514-519 curve, 7, 13 action, 574 equation, 7 't Hooft, 206 axidilaton, 359 Ansatz axion, 217, 339, 349, 359, 360, 362, 363, 478, 480, 542 for periodic SU(2) instantons, 317 axion-dilaton gravity, 359-363 for the BPS monopole, 277 and S duality, 360 Ansatz for SU(2) instantons, 274 as a truncation of N = 4, d = 4 supergravity, 361 't Hooft-Polyakov monopole, see solution, axitor, 146 't Hooft-Polyakov Banados-Teitelboim-Zanelli (BTZ) BH, see solution, BTZ Abbott-Deser approach, 106, 111, 175,176-179, 180, 372, Bekenstein-Hawking entropy, 187 394 and horizon area, see horizon, area compared with Landau-Lifshitz energy-momentum and the Euler characteristic, 245 pseudotensor, see Landau-Lifshitz energy-momentum density of BH microstates, 207 pseudotensor Bel-Robinson tensor, 171 action, 26 Belavin, see solution, BPST instanton /?-brane {a\-ai) model, see /?-brane, {a\-ai) model Belinfante tensor, 34, 35, 39, 40, 58, 59, 68, 80, 85, 130, 133 /?-brane a model, see /?-brane, a-model for a Dirac spinor, 37 /?-brane with variable tension, 502 for a spin-2 field, 82 Born-Infeld (BI), see Born-Infeld for a vector field, 35 Einstein-Hilbert, see Einstein-Hilbert action Bertotti, see solution, Robinson-Bertotti (RB) Nambu-Goto (NG), see Nambu-Goto (NG) BH,see black hole (BH) Polyakov-type, see Polyakov-type Bianchi Ramond-Neveu-Schwarz (RNS) model, see Bianchi IX gravitational instantons Ramond-Neveu-Schwarz Eguchi-Hanson solution, see solution, Eguchi-Hanson spinning particle, see Poincare, N = l,d = 1 supergravity Kaluza-Klein monopole, see solution, Kaluza-Klein supergravity theories, see supergravity theories Taub-bolt solution, see solution, Taub-bolt superparticle (Green-Schwarz), see Green-Schwarz clasification of 3d real Lie algebras, 602 ADM mass, 176,776, 189 Bianchi identities, 109, 217 of composite BH solutions, see solution, composite and gauge identities, 30, 39, 58, 59, 66, 102, 111, 114, 120, 129, 4dBHs 136, 227 of Reissner-Nordstrom BH, see solution, RN Fierz-Pauli Lagrangian, 66 of Schwarzschild's BH, see solution, Schwarzschild and Poincare dualization of the KR field, 480 AdS-CFT correspondence, 399, 536, 537, 540, 570, 573 and the dual 6-form potential of N = \,d = 11 Aharonov-Bohm phase, 254 supergravity, 452 Aichelburg, see solution, Aichelburg-Sexl shock wave contracted, 12, 13, 101, 131, 174, 214, 220, 351 angular-momentum, 268 as a gauge identity, 102, 119, 120 angular-momentum tensor, 41 for the background metric, 177 orbital, 34 for (p + 2)-form field strengths, 506, 514 spin, 34 for d-forni field strengths, 343 anholonomy coefficients, see Ricci, rotation coefficients for curvature and torsion, 8, 135, 158, 273, 602 anti-de Sitter (AdS), see de Sitter (anti-) for metric-compatible connections, 12 anti-de Sitter (AdS) spacetime, see solution, AdS for metric-compatible torsion-free connections, 13 Arnowitt, see ADM mass for embedding coordinates, 427, 440 671 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-82475-0 - Gravity and Strings Tomás Ortín Index More information 672 Index Bianchi identities (cont.) contribution to extreme BH entropy, 589 for Maxwell's field strength, 166, 167, 217, 220, 221, 225, 227, D/?-branes and O^-planes, 424 228, 257, 383 BPST instanton, see solution, BPST instanton and electric-magnetic duality, 245, 248 Brans, see Jordan-Brans-Dicke theory and electric-magnetic duality in dilaton a-model, 358 Brill, 280 and existence of a potential, 220 Brinkmann metrics, 282 and magnetic sources, 249 connection and curvature, 647 and Poincare duality, 248 BTZ, see Banados-Teitelboim-Zanelli (BTZ) BH and S duality in 4d KK theory, 311 Buscher T duality, 435-445 and S duality in dilaton-axion gravity, 360, 361 and breaking of supersymmetry, 482-484 and the Chern-Simons (CS) 3-form, 256 between Fl and W, 445 in dilaton a-model, 350, 351 between JNW and Schwarzschild solutions, 216 for RR field strengths, 458^460, 464, 487, 492 in type-II theories, 448, 485, 491, 493 and the mass parameter of Romans' theory, 465 between solutions, 551-556 for the self-dual RR 5-form, 486 transformations, 494-495 for Yang-Mills fields, 273, 276, 597 transformations of Killing spinors, 496, 562 in massive electrodynamics, 258 transformations, 437, 438 Big-Bang singularities, 195 transformations for Vielbeins, 439 Birkhoff's theorem, 189, 190, 228 black /?-branes, see solution, Schwarzschild /?-branes Cahen-Wallach symmetric spacetimes, 283, 389 black hole, 194 Cardy's formula, 578, 589 black hole (BH) Cartan axion-dilaton, see solution, axion-dilaton connection, 17, 20, 128, 132, 138 Banados-Teitelboim-Zanelli (BTZ), see solution, BTZ black first criterion (solvability), 594 hole Maurer-Cartan, see Maurer-Cartan dilaton, see solution, dilaton Riemann-Cartan spacetime, see Riemann-Cartan spacetime entropy problem, 797, 207-208 second criterion (semisimplicity), 594 information problem, 797, 206-207 Cartan-Sciama-Kibble (CSK) theory, 34, 39, 41, 113,127-140 Kerr, see solution, Kerr Cauchy horizon, see horizon, Cauchy Kerr-Newman, see solution, Kerr-Newman CFT, see conformal field theories Reissner-Nordstrom (RN), see solution, Reissner-Nordstrom Chan-Paton factors, 420, 423, 428 (RN) charge conjugation matrix, 615 Schwarzschild, see solution, Schwarzschild Chazy, see solution, Chazy-Curzon string, 573-590 Chern class SWIP, see solution, SWIP first, and the Wu-Yang monopole, 255 Bogomol'nyi (or BPS) bound, 509, 556 second, and SU(2) Yang-Mills instanton, 273, 310 and equilibrium of forces, 397, 424 Chern-Simons and supersymmetry, 373, 394-398 3-form, 132, 256, 598 in N = 1, d = 4 supergravity, 399 in N = 1, d = 10 supergravity, 498 in N = 2, d = 4 supergravity, 400 in KR field strength, 470 in N = 4, d = 4 supergravity, 400 term, 432, 530 in extended supergravities, 396 N = 1, d = 11 supergravity, 451 and the positivity of mass, 779, 398 N = 1, d = 5 supergravity, 313 and the Reissner-Nordstrom (RN) solution, 231 N = 2,d = 9 supergravity, 493 for the 't Hooft-Polyakov monopole, 276 N = 2A±T, d = 10 supergravity, 423, 487 in N = 8, d = 8 supergravity, 575 N = 2B± supergravity, 487 of string/M-theory objects, 550 in supergravity field strengths, 437, 550, 569, 570 saturated (Bogomol'nyi identity), 310 Romans' N = 2A,d = 10 supergravity, 464 Bogomol'nyi equation for SU(2) monopoles 276 Christoffel symbols, 10, 13, 20, 92, 126, 127, 210 Bogomornyi-Prasad-Sommerfield (BPS) and Weyl rescalings, 639 limit of the 't Hooft-Polyakov monopole, 276, 277, 373 Clifford Bohm, see Aharonov-Bohm phase action, 377 Boltzmann's constant, 204 algebra, 601, 611, 612, 613, 615, 616, 624, 626, 630, 631 Bonnet, see Gauss-Bonnet theorem compensator (//-), 606 Bonnor, 196, 267 Compton wavelength, 50, 115 magnetic-dipole solution, see solution, Bonnor compared with the Schwarzschild radius and Planck length, 116, Born-Infeld (BI) 206 action, 503 conformal field theories (CFTs), 573, 578, 589, 590 vector field, 435, 435, 443, 501, 564, 567 conformastationary, see metric, conformastationary dual, 549, 564 connection solitons (Blons), 549, 550, 554, 564, 566, 570 affine, 6 Boulware, 59, 78 Cartan, see Cartan, connection bound chiral, 367 Bogomol'nyi bound, see Bogomol'nyi (or BPS) bound metric-compatible, 10 BPS bound, see Bogomol'nyi (or BPS) bound spin, 78, 601 supersymmetry bound, see Bogomol'nyi (or BPS) bound continuity equation, 29 Boyer, 198 coordinate basis, 3 Boyer-Lindquist coordinates, see coordinates, Boyer-Lindquist coordinates BPS, see Bogomornyi-Prasad-Sommerfield (BPS) adapted to an isometry, 21, 99 BPS states, 370, 395-401, 408 Boyer-Lindquist, 268, 366 and the superalgebra, 395 Eddington-Finkelstein, see solution, Schwarzschild annihilated by supercharges, 394 harmonic, 199 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-82475-0 - Gravity and Strings Tomás Ortín Index More information Index 673 isotropic, 198, 216, 232, 234, 265, 271, 532-535 and the string coupling constant, 425, 487 Kruskal-Szekeres (KS), 192-193, 194, 209-211 Buscher's T-duality transformation rule, 438 Schwarzschild, see Schwarzschild, coordinates coupling to D-branes, 511 spherical, 634 coupling to fundamental branes, 511 correspondence principle, 245, 577, 578, 589 coupling to Kaluza-Klein (KK) branes, 512 cosmological constant, 102-103 coupling to solitonic branes, 511 cotangent space, 3 coupling to the D/?-brane, 434 Coulomb coupling to the string, 433 field, 200, 233 dimensional reduction on S , 436, 549 force, 218 dimensional reduction on JP, 550 covariant derivative from N = l,d = ll supergravity, 457^458, 470, 475 of world-tensor densities, 6 Dirac of world tensors, 5 conjugate, 18, 152, 468, 601, 615, 621 of Yang-Mills fields, see Yang-Mills, covariant derivative and Majorana spinors, 617 crosscaps, 412 in arbitrary signature, 628 CSK, see Cartan-Sciama-Kibble (CSK) theory conjugation matrix, 601, 613, 615, 621 curvature, see tensor, curvature in arbitrary signature, 627 curve, 7 delta function, 69, 71, 234, 518, 519 Curzon, see solution,
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