Gravity and Strings

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[506] S. F. Hassan, Nucl. Phys. B583 (2000) 431. [507] S. W. Hawking, Commun. Math. Phys. 25 (1972) 152. References 661 [508] S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge: Cambridge University Press (1973). [509] S. W. Hawking, in Black Holes, Eds. C. DeWitt and B. S. DeWitt, New York: Gordon and Breach (1973). [510] S. W. Hawking, Nature 248 (1974) 30. [511] S. W. Hawking, Commun. Math. Phys. 43 (1975) 199–220. (Reprinted in [439].) [512] S. W. Hawking, Phys. Rev. D13 (1976) 191–197. [513] S. W. Hawking, Phys. Lett. 60A (1977) 81. [514] S. W. Hawking, in General Relativity, An Einstein Centenary Survey, Eds. S. W. Hawking and W. Israel, Cambridge: Cambridge University Press (1979). [515] S. W. Hawking and G. T. Horowitz, Class. Quant. Grav. 13 (1996) 1487–1498. [516] S. W. Hawking, G. T. Horowitz, and S. F. Ross, Phys. Lett. B383 (1996) 383–389. [517] S. W. Hawking and C. J. Hunter, Phys. Rev. D59 (1999) 044025. [518] S. W. Hawking and C. J. Hunter, Class. Quant. Grav. 13 (1996) 2735–2752. [519] S. W. Hawking, C. J. Hunter and D. N. Page, hep-th/9809035. [520] S. W. Hawking and S. F. Ross, Phys. Rev. D52 (1995) 5865–5876. [521] K. Hayashi and T. Nakano, Prog. Theor. Phys. 38 (1967) 491–507. [522] K. Hayashi and T. Shirafuji, Phys. Rev. D19 (1979) 3524–3553. [523] F. W. Hehl, P. von der Heyde, G. D. Kerlick, and J. M. Nester, Rev. Mod. Phys. 48 (1976) 393–416. [524] F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne’eman, Phys. Rep. 258 (1995) 1–171. [525] K. Heiderich and W. Unruh, Phys. Rev. D38 (1988) 490–497. [526] K. R. Heiderich and W. G. Unruh, Phys. Rev. D42 (1990) 2057–2068. [527] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York (1978). [528] M. Henneaux and L. Mezincescu, Phys. Lett. B152 (1985) 340. [529] M. Henneaux and C. Teitelboim, Ann. Phys. 143 (1982) 127. [530] M. Henneaux, C. Teitelboim, and J. Zanelli Nucl. Phys. B332 (1990) 169–188. [531] M. Heusler, Black Holes Uniqueness Theorems,Cambridge: Cambridge University Press (1996). [532] M. Heusler, Helv. Phys. Acta 69 (1996) 501. [533] M. Heusler, Living Rev. Relativ. 1 (1998) 6. [534] M. Heusler and N. Straumann, Class. Quant. Grav. 10 (1993) 1299. [535] D. Hilbert, Konigl. Gesell. Wiss. Göttingen Nachr., math.-phys. Kl 295–407. [536] J. W. van Holten, in From Field Theory to Quantum Groups, Eds. B. Jancewicz and J. Sobczyk, Singapore: World Scientific (1996), pp. 173–189. [537] J. W. van Holten, Nucl. Phys. B457 (1995) 375. [538] J. W. van Holten and A. van Proeyen, J. Phys. A15 (1982) 3763. [539] C. F. Holzhey and F. Wilczek, Nucl. Phys. B380 (1992) 447–477. [540] H. Hopf, Math. Ann. 104 (1931) 637. [541] P. Hoˇrava, Nucl. Phys. B327 (1989) 461. [542] P. Hoˇrava, Phys. Lett. B231 (1989) 251. [543] P. Hoˇrava and E. Witten, Nucl. Phys. B460 (1996) 506–524. [544] P. Hoˇrava and E. Witten, Nucl. Phys. B475 (1996) 94. [545] J. H. Horne and G. T. Horowitz, Nucl. Phys. B399 (1993) 169–196. [546] G. T. Horowitz, in String Theory and Quantum Gravity, Eds. J. A. Harvey, R. Iengo, K. S. Narain, S. Randjbar-Daemi, and H. L. Verlinde, Singapore: World Scientific (1993), pp. 55–99. [547] G. T. Horowitz, in Proceedings of the Pacific Conference on Gravitation and Cosmology, Eds. Y. M. Cho, C. H. Lee, and S. W. Kim, Singapore: World Scientific (1999), pp. 46–63. [548] G. T. Horowitz, in Black Holes and Relativistic Stars, Chicago, Illinois (1998), pp. 241–266. [549] G. T. Horowitz, D. A. Lowe, and J. M. Maldacena, Phys. Rev. Lett. 77 (1996) 430. [550] G. T. Horowitz, J. M. Maldacena, and A. Strominger, Phys. Lett. B383 (1996) 151. [551] G. T. Horowitz and K. Maeda, Phys. Rev. Lett. 87 (2001) 131301.
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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
Page 1312: 636 Appendix C C.1 S 3 and S 7 as H
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Page 1320: The metric Appendix F Connections a
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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 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
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