Gravity and Strings

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[411] D. V. Gal’tsov and O. V. Kechkin, Phys. Rev. D54 (1996) 1656–1666. [412] D. V. Gal’tsov and P. S. Letelier, Phys. Rev. D55 (1997) 3580. [413] D. V. Gal’tsov and S. A. Sharakin, Phys. Lett. B399 (1997) 250–257. References 659 [414] R. Gambini and J. Pullin, Loops, Knots, Gauge Theories and Quantum Gravity, Cambridge: Cambridge University Press (1996). [415] A. Garcia, D. V. Gal’tsov, and O. V. Kechkin, Phys. Rev. Lett. 74 (1995) 1276–1279. [416] D. Garfinkle, G. Horowitz and A. Strominger, Phys. Rev. D43 (1991) 3140. Erratum Phys. Rev. D45 (1992) 3888. [417] J. P. Gauntlett, in Dualities of Gauge and String Theories, Eds. Y. M. Cho and S. Nam, Singapore: World Scientific (1998), pp. 146–193. [418] J. P. Gauntlett, G. W. Gibbons, G. Papadopoulos, and P. K. Townsend, Nucl. Phys. B500 (1997) 133. [419] J. P. Gauntlett, J. Gomis, and P. K. Townsend, JHEP 9801 (1998) 003. [420] J. P. Gauntlett, J. B. Gutowski, C. M. Hull, S. Pakis, and H. S. Reall, hep-th/0209114. [421] J. P. Gauntlett, D. A. Kastor, and J. Traschen, Nucl. Phys. B478 (1996) 544. [422] J. P. Gauntlett, R. C. Myers, and P. K. Townsend, Phys. Rev. D59 (1999) 025001. [423] J. P. Gauntlett and S. Pakis, JHEP 0304 (2003) 039. [424] S. P. Gavrilov and D. M. Gitman, Int. J. Mod. Phys. A15 (2000) 4499. [425] H. Georgi and S. L. Glashow, Phys. Rev. Lett. 28 (1972) 1494. [426] J. Gheerardyn and P. Meessen, Phys. Lett. B525 (2002) 322. [427] F. Giani and M. Pernici, Phys. Rev. D30 (1984) 325. [428] G. W. Gibbons, Commun Math. Phys. 35 (1974) 13–23. [429] G. W. Gibbons, Commun. Math. Phys. 44 (1975) 245–264. [430] G. W. Gibbons, Proc. Roy. Soc. London A372 (1980) 535. [431] G. W. Gibbons, Notes of Lectures given at the 1980 Summer Institute of the Ecole Normale Supérieure, LPT, Paris, France, August 4–23, 1980 (unpublished). [432] G. W. Gibbons, Nucl. Phys. B207 (1982) 337. [433] G. W. Gibbons, in Supersymmetry, Supergravity and Related Topics, Eds. F. del Águila, J. de Azcárraga and L. Ibáñez, Singapore: World Scientific (1985), p. 147. [434] G. W. Gibbons, Nucl. Phys. B514 (1998) 603. [435] G. W. Gibbons, M. B. Green, and M. J. Perry. Phys. Lett. B370 (1996) 37–44. [436] G. W. Gibbons and S. W. Hawking, Phys. Rev. D15 (1977) 2752. (Reprinted in [439].) [437] G. W. Gibbons and S. W. Hawking, Phys. Lett. 78B (1978) 430–432. (Reprinted in [439].) [438] G. W. Gibbons and S. W. Hawking, Commun. Math. Phys. 66 (1979) 291. (Reprinted in [439].) [439] G. W. Gibbons and S. W. Hawking (Eds.), Euclidean Quantum Gravity, Singapore: World Scientific (1993). [440] G. W. Gibbons and C. A. R. Herdeiro, Class. Quant. Grav. 16 (1999) 3619–3652. [441] G. W. Gibbons, G. T. Horowitz, and P. K. Townsend, Class. Quant. Grav. 12 (1995) 297–318. [442] G. W. Gibbons and C. M. Hull, Phys. Lett. 109B (1982) 190. [443] G. W. Gibbons, C. M. Hull, and N. P. Warner, Nucl. Phys. B218 (1983) 173–190. [444] G. W. Gibbons, D. Ida, and T. Shiromizu, Phys. Rev. Lett. 89 (2002) 041101. [445] G. W. Gibbons and R. E. Kallosh, Phys. Rev. D51 (1995) 2839–2862. [446] G. W. Gibbons, R. Kallosh, and B. Kol, Phys. Rev. Lett. 77 (1996) 4992–4995. [447] G. W. Gibbons and K. Maeda, Nucl. Phys. B298 (1988) 741. [448] G. W. Gibbons and M. J. Perry, Phys. Rev. D22 (1980) 313. [449] G. W. Gibbons and C. N. Pope, Commun. Math. Phys. 66 (1979) 267–290. (Reprinted in [439].) [450] G. W. Gibbons and D. A. Rasheed, Nucl. Phys. B454 (1995) 185. [451] G. W. Gibbons and D. A. Rasheed, Phys. Lett. B365 (1996) 46. [452] G. W. Gibbons and P. K. Townsend, Phys. Rev. Lett. 71 (1993) 3754–3757. [453] S. B. Giddings and A. Strominger, Phys. Lett. B230 (1989) 46. [454] R. Gilmore, Lie Groups, Lie Algebras and Some of Their Applications,New York: Wiley (1974). [455] P. Ginsparg, in Fields, Strings and Critical Phenomena, Eds. E. Brézin and J. Zinn-Justin, Amsterdam: North Holland (1990), pp. 1–168. [456] A. Giveon, M. Porrati, and E. Rabinovici, Phys. Rep. 244 (1994) 77–202. [457] F. Gliozzi, J. Scherk, and D. Olive, Nucl. Phys. B122 (1977) 253–290.
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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
Page 1308: Appendix C n-Spheres An n-dimension
Page 1312: 636 Appendix C C.1 S 3 and S 7 as H
Page 1316: Appendix D Palatini’s identity Th
Page 1320: The metric Appendix F Connections a
Page 1324: 642 Appendix F The components of th
Page 1328: 644 Appendix F and the Ricci scalar
Page 1332: 646 Appendix F The non-vanishing co
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 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
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