Gravity and Strings

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[889] G. ’t Hooft, Nucl. Phys. B62 (1973) 444–460. [890] G. ’t Hooft, Nucl. Phys. B79 (1974) 276–284. [891] G. ’t Hooft and M. Veltman, Ann. Inst. Henri Poincaré 20 (1974) 69. [892] A. Trautman, Int. J. Theor. Phys. 16 (1977) 561. [893] K. P. Tod, Phys. Lett. 121B, (1981) 241. [894] K. P. Tod, Class. Quant. Grav. 12 (1995) 1801–1820. [895] M. A. Tonnelat, La théorie du champ unifié d’Einstein,Paris: Gauthier-Villars (1955). [896] P. K. Townsend, Phys. Lett. B277 (1992) 285. [897] P. K. Townsend, Phys. Lett. B350 (1995) 184. References 669 [898] P. K. Townsend, in PASCOS/Johns Hopkins 1995, Eds. J. A. Bagger, G. K. Domokos, A. F. Falk, and S. Kövesi-Domokos, Singapore: World Scientific (1996), pp. 271–286. [899] P. K. Townsend, Phys. Lett. B373 (1996) 68. [900] P. K. Townsend, Nucl. Phys. Proc. Suppl. B475 (1996). [901] P. K. Townsend, in Trieste 1996 Summer School in High Energy Physics and Cosmology, Eds. E. Gava, A. Masiero, K. S. Narain, S. Randjbar-Daemi, and Q. Shaft, Singapore: World Scientific (1997), pp. 385–438. [902] P. K. Townsend, Phys. Lett. B409 (1997) 131. [903] P. K. Townsend, gr-qc/9707012. [904] P. K. Townsend, Nucl. Phys. Proc. Suppl. 67 (1998) 88. [905] P. K. Townsend, in Strings, Branes and Dualities, Eds. L. Baulieu, P. Di Francesco, M. Douglas, V. Kazakov, M. Picco, and P. Windey, Dordrecht: Kluwer (1999), pp. 141–177. [906] P. K. Townsend, hep-th/9901102. [907] J. Traschen, in Mathematical Methods of Physics, Eds. A. Bytsenko and F. Williams, Singapore: World Scientific (2000). [908] A. A. Tseytlin, Nucl. Phys. B475 (1996) 149. [909] A. A. Tseytlin, in The Many Faces of the Superworld, Ed. M. A. Shifman, Singapore: World Scientific (2000), pp. 417–452. [910] H. J. de Vega, M. Ramón Medrano, and N. Sánchez, Nucl. Phys. B374 (1992) 425. [911] A. E. M. van de Ven, Nucl. Phys. B378 (1992) 309–366. [912] P. van Nieuwenhuizen, Phys. Rep. 68 (1981) 189–398. [913] P. van Nieuwenhuizen, in Supergravity ’81, Cambridge: Cambridge University Press (1982), pp. 151–196. [914] P. van Nieuwenhuizen, in 1975 Marcel Grossmann Meeting on General Relativity, Oxford: Oxford University Press (1977), pp. 1–26. [915] A. van Proeyen, in Spring School on Quantum Field Theory: Supersymmetry and Superstrings. [916] A. van Proeyen, hep-th/0301005. [917] W. G. Unruh, Phys. Rev. D10 (1974) 3194–3205. [918] R. Utiyama, Phys. Rev. 101 (1956) 1597. [919] M. A. Vandyck, Gen. Relativ. Gravit. 20 (1988) 261. [920] M. A. Vandyck, Gen. Relativ. Gravit. 20 (1988) 905. [921] L. Vanzo, Phys. Rev. D56 (1997) 6475–6483. [922] M. A. G. Veltman, in Methods in Field Theory, Eds. R. Balian and J. Zinn-Justin, Amsterdam: North-Holland (1976), p. 265. [923] M. A. G. Veltman, Nucl. Phys. B319 (1989) 253–270. [924] H. Vermeil, Nachr. Ges. Wiss. Göttingen (1917) 334. [925] A. Volovich, Nucl. Phys. B492 (1997) 235–248. [926] P. von der Heyde, Z. Naturforsch. 31a (1976) 1725–1726. [927] S. Wadia, hep-th/0011286. [928] R. M. Wald, Phys. Rev. Lett. 26 (1971) 1653–1655. [929] R. M. Wald, Phys. Rev. D6 (1972) 1476–1479. [930] R. M. Wald, Ann. Phys. 83 (1974) 548. [931] R. M. Wald, in Black Holes, Gravitational Radiation and the Universe, Eds. B. R. Iyer, B. Bhawal, and C. V. Vishveshwara, Dordrecht: Kluwer (1998), pp. 69–85. [932] R. Wald, General Relativity, Chicago, Illinois: The University of Chicago Press (1984). [933] R. M. Wald, Phys. Rev. D33 (1986) 3613–3625. [934] R. M. Wald, Class. Quant. Grav. 4 (1987) 1279.
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Gravity and Strings One appealing f
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Gravity and Strings TOMÁS ORTÍN S
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To Marimar, Diego, and Tomás, the
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x Contents 3.1.1 Scalar gravity cou
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xii Contents 8.7.4 Dyons and the DS
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xiv Contents 14.3.2 Open bosonic st
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xvi Contents Appendix A Lie groups,
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Preface String theory has lived for
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Part I Introduction to gravity and
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4 Differential geometry function 1
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6 Differential geometry and on weig
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8 Differential geometry We can also
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10 Differential geometry where ρ
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12 Differential geometry a metric-c
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14 Differential geometry scalar R,
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16 Differential geometry Local GL(d
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18 Differential geometry In the sec
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20 Differential geometry where ω(e
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22 Differential geometry We define
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24 Differential geometry Since ⋆d
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2 Noether’s theorems In the next
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28 Noether’s theorems where x ′
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30 Noether’s theorems First, obse
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32 Noether’s theorems Sometimes i
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34 Noether’s theorems According t
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36 Noether’s theorems which is th
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38 Noether’s theorems Furthermore
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40 Noether’s theorems The Rosenfe
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42 Noether’s theorems is invarian
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44 Noether’s theorems In this way
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46 A perturbative introduction to g
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100 A perturbative introduction to
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4 Action principles for gravity A m
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116 Action principles for gravity w
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120 Action principles for gravity T
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122 Action principles for gravity a
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124 Action principles for gravity F
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126 Action principles for gravity s
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128 Action principles for gravity t
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130 Action principles for gravity a
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132 Action principles for gravity i
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134 Action principles for gravity f
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138 Action principles for gravity W
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142 Action principles for gravity t
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144 Action principles for gravity W
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5 N = 1, 2, d = 4 supergravities In
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152 N = 1, 2, d = 4 supergravities
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172 Conserved charges in general re
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Part II Gravitating point-particles
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188 The Schwarzschild black hole Th
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190 The Schwarzschild black hole st
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192 The Schwarzschild black hole V
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194 The Schwarzschild black hole I
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196 The Schwarzschild black hole by
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198 The Schwarzschild black hole 14
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200 The Schwarzschild black hole an
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204 The Schwarzschild black hole T
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206 The Schwarzschild black hole C
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208 The Schwarzschild black hole As
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210 The Schwarzschild black hole ne
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214 The Reissner-Nordström black h
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268 The Taub-NUT solution The charg
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270 The Taub-NUT solution 4. This m
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272 The Taub-NUT solution This solu
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274 The Taub-NUT solution Four-dime
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276 The Taub-NUT solution become th
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278 The Taub-NUT solution All Ricci
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280 The Taub-NUT solution The elect
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10 Gravitational pp-waves As we saw
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284 Gravitational pp-waves The Heis
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286 Gravitational pp-waves The spec
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288 Gravitational pp-waves The equa
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11 The Kaluza-Klein black hole Kalu
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292 The Kaluza-Klein black hole Spa
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294 The Kaluza-Klein black hole Tab
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296 The Kaluza-Klein black hole The
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298 The Kaluza-Klein black hole whi
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300 The Kaluza-Klein black hole As
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304 The Kaluza-Klein black hole dim
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306 The Kaluza-Klein black hole We
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308 The Kaluza-Klein black hole Wha
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310 The Kaluza-Klein black hole and
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312 The Kaluza-Klein black hole the
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314 The Kaluza-Klein black hole KK
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316 The Kaluza-Klein black hole SUG
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318 The Kaluza-Klein black hole ˆd
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320 The Kaluza-Klein black hole whi
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326 The Kaluza-Klein black hole gen
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328 The Kaluza-Klein black hole Low
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332 The Kaluza-Klein black hole has
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334 The Kaluza-Klein black hole whe
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336 The Kaluza-Klein black hole ω1
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338 The Kaluza-Klein black hole com
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342 The Kaluza-Klein black hole whe
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344 The Kaluza-Klein black hole m
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346 The Kaluza-Klein black hole It
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348 The Kaluza-Klein black hole 11.
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350 Dilaton and dilaton/axion black
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370 Unbroken supersymmetry theories
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372 Unbroken supersymmetry conserve
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374 Unbroken supersymmetry infinite
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376 Unbroken supersymmetry ν1··
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378 Unbroken supersymmetry transfor
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380 Unbroken supersymmetry The Kill
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382 Unbroken supersymmetry and, usi
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384 Unbroken supersymmetry In this
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386 Unbroken supersymmetry The dual
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388 Unbroken supersymmetry To calcu
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390 Unbroken supersymmetry The supe
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392 Unbroken supersymmetry transfor
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394 Unbroken supersymmetry AdS 2 ¥
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396 Unbroken supersymmetry precisel
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398 Unbroken supersymmetry and prov
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400 Unbroken supersymmetry Observe
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Part III Gravitating extended objec
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406 String theory String Theory Sol
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408 String theory modes behave unde
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410 String theory γij. The so-call
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412 String theory This term does no
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414 String theory where ˜Diɛ = (
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416 String theory Table 14.1. A bra
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418 String theory multiplets charac
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420 String theory Observe that the
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422 String theory Table 14.2. In th
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424 String theory 14.2.3 D-Branes a
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426 String theory 14.3 Compactifica
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428 String theory This description
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15 The string effective action and
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448 From eleven to four dimensions
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486 The type-IIB superstring and ty
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18 Extended objects Introduction In
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502 Extended objects spacetime, S (
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504 Extended objects Let us assume
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506 Extended objects 18.1.2 Charged
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508 Extended objects Fig. 18.1. Ope
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510 Extended objects We have introd
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512 Extended objects Their mass is
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514 Extended objects p-brane soluti
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516 Extended objects In general, th
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518 Extended objects The equations
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19 The extended objects of string t
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522 The extended objects of string
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M2 M5 d = 11 KK7 KK9 WM D8 D6 D2 D4
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574 String black holes in four and
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592 Appendix A Similarly, we can de
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594 Appendix A We can now introduce
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596 Appendix A If we now consider l
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598 Appendix A There is another inv
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600 Appendix A Using this represent
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602 Appendix A As usual, the curvat
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604 Appendix A With the Euler-angle
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606 Appendix A which is a function
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608 Appendix A A.4.1 H-covariant de
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610 Appendix A and the curvature, w
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612 Appendix B Lorentz transformati
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614 Appendix B provide a representa
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616 Appendix B When d is even, both
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618 Appendix B Table B.1. Spinors t
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620 Appendix B Let us now consider
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622 Appendix B is equivalent to req
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624 Appendix B However, it is possi
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626 Appendix B B.1.11 Six dimension
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628 Appendix B Table B.2. Possible
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630 Appendix B representation of th
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632 Appendix B Although these two r
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Appendix C n-Spheres An n-dimension
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636 Appendix C C.1 S 3 and S 7 as H
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Appendix D Palatini’s identity Th
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The metric Appendix F Connections a
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642 Appendix F The components of th
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Page 1336: Appendix G The harmonic operator on
Page 1340: [1] L. F. Abbott and S. Deser, Nucl
Page 1344: 652 References [80] I. Bandos, K. L
Page 1348: 654 References [176] B. D. Boulware
Page 1352: 656 References [269] H. E. J. Curzo
Page 1356: 658 References [364] A. Einstein, T
Page 1360: 660 References [458] P. Goddard, J.
Page 1364: 662 References [552] G. T. Horowitz
Page 1368: 664 References [648] J. P. S. Lemos
Page 1372: 666 References [745] T. Ortín, Nuc
Page 1376: 668 References [841] J. Schwinger,
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
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