Gravity and Strings

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[222] L. Castellani, R. D’Auria, and S. Ferrara, Class. Quant. Grav. 1 (1990) 317. References 655 [223] M. Cederwall, A. von Gussich, B. E. Nilsson, and A. Westerberg, Nucl. Phys. B490 (1997) 163. [224] M. Cederwall, A. von Gussich, B. E. Nilsson, P. Sundell, and A. Westerberg, Nucl. Phys. B490 (1997) 179. [225] A. Ceresole, R. D’Auria, S. Ferrara, and A. Van Proeyen, Nucl. Phys. 444 (1995) 92. [226] A. Chamseddine, Nucl. Phys. B185 (1981) 403–415. [227] A. H. Chamseddine, Ann. Phys. 113 (1978) 219. [228] A. H. Chamseddine, S. Ferrara, G. W. Gibbons, and R. Kallosh, Phys. Rev. D55 (1997) 3647. [229] A. H. Chamseddine, J. M. Figueroa-O’Farrill, and W. Sabra, Six-Dimensional Supergravity Vacua and Anti-Selfdual Lorentzian Lie Groups, hep-th/0306278. [230] A. H. Chamseddine and H. Nicolai, Phys. Lett. B96 (1980) 89. [231] A. H. Chamseddine and P. C. West, Nucl. Phys. B129 (1977) 39. [232] S. Chandrasekhar, The Mathemetical Theory of Black Holes, Oxford: Clarendon Press (1983). [233] G. F. Chapline and N. S. Manton, Phys. Lett. B120 (1983) 105. [234] J. E. Chase, Commun. Math. Phys. 19 (1970) 276. [235] J. Chazy, Bull. Soc. Math. France 52 (1924) 17. [236] S. S. Chern, Ann. Math. 46 (1945) 674–684. [237] Y. M. Cho, Phys. Rev. D14 (1976) 2521. [238] Y. M. Cho and S. W. Zoh, Phys. Rev. D46 (1992) R2290. [239] Y. M. Cho and S. W. Zoh, Phys. Rev. D46 (1992) 3483. [240] Y. Choquet-Bruhat, C. DeWitt-Morette, and M. Dillard-Bleick, Analysis, Manifolds and Physics, Amsterdam: Elsevier (1977). [241] D. Christodoulou, Ph.D. Thesis, Princeton University (unpublished). [242] J. Ciufolini and J. A. Wheeler, Gravitation and Inertia, Princeton, New Jersey: Princeton University Press (1995). [243] C. J. S. Clarke, The Analysis of Space-Time Singularities, Cambridge: Cambridge University Press (1993). [244] C. J. S. Clarke, Class. Quant. Grav. 10 (1993) 1375. [245] G. Clément and D. V. Gal’tsov, Phys. Rev. D54 (1996) 6136. [246] S. Coleman, in Gauge Theories in High Energy Physics, Eds. M. K. Gaillard and R. F. Stora, Amsterdam: North-Holland (1983). [247] S. Coleman and R. Jackiw, Ann. Phys. 67 (1971) 552. [248] S. Coleman, S. Parke, A. Neveu, and C. M. Sommerfield, Phys. Rev. D15 (1977) 544–545. [249] S. Coleman, J. Preskill, and F. Wilczek, Nucl. Phys. B378 (1992) 175. [250] A. A. Coley, Phys. Rev. Lett. 89 (2002) 281601. [251] P. A. Collins and R. W. Tucker, Nucl. Phys. B121 (1977) 307. [252] R. Coquereaux and A. Jadczyk, Riemannian Geometry, Fiber Bundles, Kaluza–Klein Theories and All That. Singapore: World Scientific, (1988). [253] N. J. Cornish and J. W. Moffat, Phys. Rev. D47 (1993) 4421–4424. [254] M. S. Costa, Nucl. Phys. B490 (1997) 202–216. [255] M. S. Costa, Nucl. Phys. B495 (1997) 195–205. [256] M. S. Costa and G. Papadopoulos, Nucl. Phys. B510 (1998) 217–231. [257] M. S. Costa and M. J. Perry, Nucl. Phys. B591 (2000) 469–487. [258] P. M. Cowdall, hep-th/0009016. [259] J. D. E. Creighton and R. B. Mann, Phys. Rev. D52 (1995) 4569. [260] J. D. E. Creighton and R. B. Mann, gr-qc/9511012. [261] E. Cremmer, in Superspace & Supergravity, Eds. S. W. Hawking and M. Roček, Cambridge: Cambridge University Press (1981), p. 267. [262] E. Cremmer and S. Ferrara, Phys. Lett. B91 (1980) 61. [263] E. Cremmer and B. Julia, Nucl. Phys. B159 (1979) 141. [264] E. Cremmer, B. Julia, and J. Scherk, Phys. Lett. 76B (1978) 409. [265] E. Cremmer, C. Kounnas, A. Van Proeyen, J. P. Derendinger, S. Ferrara, B. de Wit, and L. Girardello, Nucl. Phys. 250 (1985) 385. [266] E. Cremmer, J. Scherk, and S. Ferrara, Phys. Lett. 74B (1978) 64. [267] J. F. Cornwell, Group Theory in Physics volumes 1, 2, and 3, London: Academic Press (1989). [268] P. T. Chru´sciel, Contemp. Math. 170 (1994) 23–49.
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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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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 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
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Dp, 538 compactified on T 6 , 577 c
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extended, 121, 150, 160-163, 379, 3
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