Gravity and Strings

More documents

Recommendations

Info

Gamma matrices and spinors 633 labeled by the index â = (â, 4) which we raise and lower with the SO(2, 4) metric ˆη â ˆb = diag(++−−−−). Itcan be proved that these matrices are an orthonormal basis in the space of real 4 × 4 antisymmetric matrices with the trace as scalar product (rasing and lowering indices with C): nâ αβn ˆb βα = 2δâ ˆb , (B.146) n â γδ nâ αβ =−2δ[γδ] [αβ].
Page 2:
Gravity and Strings One appealing f
Page 10:
Gravity and Strings TOMÁS ORTÍN S
Page 14:
To Marimar, Diego, and Tomás, the
Page 20:
x Contents 3.1.1 Scalar gravity cou
Page 24:
xii Contents 8.7.4 Dyons and the DS
Page 28:
xiv Contents 14.3.2 Open bosonic st
Page 32:
xvi Contents Appendix A Lie groups,
Page 38:
Preface String theory has lived for
Page 42:
Part I Introduction to gravity and
Page 48:
4 Differential geometry function 1
Page 52:
6 Differential geometry and on weig
Page 56:
8 Differential geometry We can also
Page 60:
10 Differential geometry where ρ
Page 64:
12 Differential geometry a metric-c
Page 68:
14 Differential geometry scalar R,
Page 72:
16 Differential geometry Local GL(d
Page 76:
18 Differential geometry In the sec
Page 80:
20 Differential geometry where ω(e
Page 84:
22 Differential geometry We define
Page 88:
24 Differential geometry Since ⋆d
Page 92:
2 Noether’s theorems In the next
Page 96:
28 Noether’s theorems where x ′
Page 100:
30 Noether’s theorems First, obse
Page 104:
32 Noether’s theorems Sometimes i
Page 108:
34 Noether’s theorems According t
Page 112:
36 Noether’s theorems which is th
Page 116:
38 Noether’s theorems Furthermore
Page 120:
40 Noether’s theorems The Rosenfe
Page 124:
42 Noether’s theorems is invarian
Page 128:
44 Noether’s theorems In this way
Page 132:
46 A perturbative introduction to g
Page 136:
Page 140:
Page 144:
Page 148:
Page 152:
Page 156:
Page 160:
Page 164:
Page 168:
Page 172:
Page 176:
Page 180:
Page 184:
Page 188:
Page 192:
Page 196:
Page 200:
Page 204:
Page 208:
Page 212:
Page 216:
Page 220:
Page 224:
Page 228:
Page 232:
Page 236:
Page 240:
100 A perturbative introduction to
Page 244:
Page 248:
Page 252:
Page 256:
Page 260:
Page 264:
Page 268:
4 Action principles for gravity A m
Page 272:
116 Action principles for gravity w
Page 276:
Page 280:
120 Action principles for gravity T
Page 284:
122 Action principles for gravity a
Page 288:
124 Action principles for gravity F
Page 292:
126 Action principles for gravity s
Page 296:
128 Action principles for gravity t
Page 300:
130 Action principles for gravity a
Page 304:
132 Action principles for gravity i
Page 308:
134 Action principles for gravity f
Page 312:
Page 316:
138 Action principles for gravity W
Page 320:
Page 324:
142 Action principles for gravity t
Page 328:
144 Action principles for gravity W
Page 332:
Page 336:
Page 340:
5 N = 1, 2, d = 4 supergravities In
Page 344:
152 N = 1, 2, d = 4 supergravities
Page 348:
Page 352:
Page 356:
Page 360:
Page 364:
Page 368:
Page 372:
Page 376:
Page 380:
Page 384:
172 Conserved charges in general re
Page 388:
Page 392:
Page 396:
Page 400:
Page 404:
Page 410:
Part II Gravitating point-particles
Page 416:
188 The Schwarzschild black hole Th
Page 420:
190 The Schwarzschild black hole st
Page 424:
192 The Schwarzschild black hole V
Page 428:
194 The Schwarzschild black hole I
Page 432:
196 The Schwarzschild black hole by
Page 436:
198 The Schwarzschild black hole 14
Page 440:
200 The Schwarzschild black hole an
Page 444:
Page 448:
204 The Schwarzschild black hole T
Page 452:
206 The Schwarzschild black hole C
Page 456:
208 The Schwarzschild black hole As
Page 460:
210 The Schwarzschild black hole ne
Page 464:
Page 468:
214 The Reissner-Nordström black h
Page 472:
Page 476:
Page 480:
Page 484:
Page 488:
Page 492:
Page 496:
Page 500:
Page 504:
Page 508:
Page 512:
Page 516:
Page 520:
Page 524:
Page 528:
Page 532:
Page 536:
Page 540:
Page 544:
Page 548:
Page 552:
Page 556:
Page 560:
Page 564:
Page 568:
Page 572:
Page 576:
268 The Taub-NUT solution The charg
Page 580:
270 The Taub-NUT solution 4. This m
Page 584:
272 The Taub-NUT solution This solu
Page 588:
274 The Taub-NUT solution Four-dime
Page 592:
276 The Taub-NUT solution become th
Page 596:
278 The Taub-NUT solution All Ricci
Page 600:
280 The Taub-NUT solution The elect
Page 604:
10 Gravitational pp-waves As we saw
Page 608:
284 Gravitational pp-waves The Heis
Page 612:
286 Gravitational pp-waves The spec
Page 616:
288 Gravitational pp-waves The equa
Page 620:
11 The Kaluza-Klein black hole Kalu
Page 624:
292 The Kaluza-Klein black hole Spa
Page 628:
294 The Kaluza-Klein black hole Tab
Page 632:
296 The Kaluza-Klein black hole The
Page 636:
298 The Kaluza-Klein black hole whi
Page 640:
300 The Kaluza-Klein black hole As
Page 644:
Page 648:
304 The Kaluza-Klein black hole dim
Page 652:
306 The Kaluza-Klein black hole We
Page 656:
308 The Kaluza-Klein black hole Wha
Page 660:
310 The Kaluza-Klein black hole and
Page 664:
312 The Kaluza-Klein black hole the
Page 668:
314 The Kaluza-Klein black hole KK
Page 672:
316 The Kaluza-Klein black hole SUG
Page 676:
318 The Kaluza-Klein black hole ˆd
Page 680:
320 The Kaluza-Klein black hole whi
Page 684:
Page 688:
Page 692:
326 The Kaluza-Klein black hole gen
Page 696:
328 The Kaluza-Klein black hole Low
Page 700:
Page 704:
332 The Kaluza-Klein black hole has
Page 708:
334 The Kaluza-Klein black hole whe
Page 712:
336 The Kaluza-Klein black hole ω1
Page 716:
338 The Kaluza-Klein black hole com
Page 720:
Page 724:
342 The Kaluza-Klein black hole whe
Page 728:
344 The Kaluza-Klein black hole m
Page 732:
346 The Kaluza-Klein black hole It
Page 736:
348 The Kaluza-Klein black hole 11.
Page 740:
350 Dilaton and dilaton/axion black
Page 744:
Page 748:
Page 752:
Page 756:
Page 760:
Page 764:
Page 768:
Page 772:
Page 776:
Page 780:
370 Unbroken supersymmetry theories
Page 784:
372 Unbroken supersymmetry conserve
Page 788:
374 Unbroken supersymmetry infinite
Page 792:
376 Unbroken supersymmetry ν1··
Page 796:
378 Unbroken supersymmetry transfor
Page 800:
380 Unbroken supersymmetry The Kill
Page 804:
382 Unbroken supersymmetry and, usi
Page 808:
384 Unbroken supersymmetry In this
Page 812:
386 Unbroken supersymmetry The dual
Page 816:
388 Unbroken supersymmetry To calcu
Page 820:
390 Unbroken supersymmetry The supe
Page 824:
392 Unbroken supersymmetry transfor
Page 828:
394 Unbroken supersymmetry AdS 2 ¥
Page 832:
396 Unbroken supersymmetry precisel
Page 836:
398 Unbroken supersymmetry and prov
Page 840:
400 Unbroken supersymmetry Observe
Page 846:
Part III Gravitating extended objec
Page 852:
406 String theory String Theory Sol
Page 856:
408 String theory modes behave unde
Page 860:
410 String theory γij. The so-call
Page 864:
412 String theory This term does no
Page 868:
414 String theory where ˜Diɛ = (
Page 872:
416 String theory Table 14.1. A bra
Page 876:
418 String theory multiplets charac
Page 880:
420 String theory Observe that the
Page 884:
422 String theory Table 14.2. In th
Page 888:
424 String theory 14.2.3 D-Branes a
Page 892:
426 String theory 14.3 Compactifica
Page 896:
428 String theory This description
Page 900:
15 The string effective action and
Page 904:
Page 908:
Page 912:
Page 916:
Page 920:
Page 924:
Page 928:
Page 932:
Page 936:
448 From eleven to four dimensions
Page 940:
Page 944:
Page 948:
Page 952:
Page 956:
Page 960:
Page 964:
Page 968:
Page 972:
Page 976:
Page 980:
Page 984:
Page 988:
Page 992:
Page 996:
Page 1000:
Page 1004:
Page 1008:
Page 1012:
486 The type-IIB superstring and ty
Page 1016:
Page 1020:
Page 1024:
Page 1028:
Page 1032:
Page 1036:
Page 1040:
18 Extended objects Introduction In
Page 1044:
502 Extended objects spacetime, S (
Page 1048:
504 Extended objects Let us assume
Page 1052:
506 Extended objects 18.1.2 Charged
Page 1056:
508 Extended objects Fig. 18.1. Ope
Page 1060:
510 Extended objects We have introd
Page 1064:
512 Extended objects Their mass is
Page 1068:
514 Extended objects p-brane soluti
Page 1072:
516 Extended objects In general, th
Page 1076:
518 Extended objects The equations
Page 1080:
19 The extended objects of string t
Page 1084:
522 The extended objects of string
Page 1088:
Page 1092:
Page 1096:
Page 1100:
Page 1104:
Page 1108:
Page 1112:
Page 1116:
Page 1120:
Page 1124:
Page 1128:
Page 1132:
Page 1136:
Page 1140:
Page 1144:
M2 M5 d = 11 KK7 KK9 WM D8 D6 D2 D4
Page 1148:
Page 1152:
Page 1156:
Page 1160:
Page 1164:
Page 1168:
Page 1172:
Page 1176:
Page 1180:
Page 1184:
Page 1188:
574 String black holes in four and
Page 1192:
Page 1196:
Page 1200:
Page 1204:
Page 1208:
Page 1212:
Page 1216:
Page 1220:
Page 1224:
592 Appendix A Similarly, we can de
Page 1228:
594 Appendix A We can now introduce
Page 1232:
596 Appendix A If we now consider l
Page 1236:
598 Appendix A There is another inv
Page 1240:
600 Appendix A Using this represent
Page 1244:
602 Appendix A As usual, the curvat
Page 1248:
604 Appendix A With the Euler-angle
Page 1252:
606 Appendix A which is a function
Page 1256: 608 Appendix A A.4.1 H-covariant de
Page 1260: 610 Appendix A and the curvature, w
Page 1264: 612 Appendix B Lorentz transformati
Page 1268: 614 Appendix B provide a representa
Page 1272: 616 Appendix B When d is even, both
Page 1276: 618 Appendix B Table B.1. Spinors t
Page 1280: 620 Appendix B Let us now consider
Page 1284: 622 Appendix B is equivalent to req
Page 1288: 624 Appendix B However, it is possi
Page 1292: 626 Appendix B B.1.11 Six dimension
Page 1296: 628 Appendix B Table B.2. Possible
Page 1300: 630 Appendix B representation of th
Page 1304: 632 Appendix B Although these two r
Page 1310: Appendix C 635 For some purposes, s
Page 1314: Appendix C 637 C.2 Squashed S 3 and
Page 1318: Appendix E Conformal rescalings If
Page 1322: Connections and curvature component
Page 1326: and the Ricci scalar is given by We
Page 1330: Connections and curvature component
Page 1334: The Ricci scalar is Connections and
Page 1338: The harmonic operator on R 3 × S 1
Page 1342: [35] E. Álvarez, L. Álvarez-Gaum
Page 1346: [128] E. Bergshoeff, R. Kallosh, T.
Page 1350: [222] L. Castellani, R. D’Auria,
Page 1354: [316] S. Deser and B. Zumino, Phys.
Page 1358:
[411] D. V. Gal’tsov and O. V. Ke
Page 1362:
[506] S. F. Hassan, Nucl. Phys. B58
Page 1366:
References 663 [600] J. M. Izquierd
Page 1370:
[696] R. R. Metsaev and A. A. Tseyt
Page 1374:
[793] H. Quevedo, Fortschr. Phys. 3
Page 1378:
[889] G. ’t Hooft, Nucl. Phys. B6
Page 1382:
Index Page numbers in italic are th
Page 1386:
isotropic, 198, 216, 232, 234, 265,
Page 1390:
Noether method, 78 first-order form
Page 1394:
integrability equation in N = 2, d
Page 1398:
Newman-Penrose formalism, see Newma
Page 1402:
Dp, 538 compactified on T 6 , 577 c
Page 1406:
extended, 121, 150, 160-163, 379, 3
show all

Gravity and Strings

Create successful ePaper yourself

Delete template?

Save as template?