Gravity and Strings

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[793] H. Quevedo, Fortschr. Phys. 38 (1990) 733. [794] A. Rajaraman, JHEP 0109 (2001) 018. References 667 [795] P. Ramond, Field Theory: A Modern Primer, Reading, Massachussets: Benjamin/Cummings (1981). [796] P. Ramond, Phys. Rev. D3 (1971) 2415. [797] L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999) 3370. [798] L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999) 4690. [799] J. Rayski, Acta Phys. Polon 27 (1965) 89. [800] H. S. Reall, Phys. Rev. D64 (2001) 044005. [801] M. Rees, in Black Holes and Relativistic Stars, Ed. R. M. Wald, Chicago, Illinois: The University of Chicago Press (1998). [802] H. Reissner, Ann. Phys. 50 (1916) 106. [803] S. J. Rey, Phys. Rev. D43, 526 (1991). [804] F. Riccioni, hep-th/0301021. [805] M. Rocek and E. Verlinde, Nucl. Phys. B373 (1992) 630 [806] M. Rogatko, Class. Quant. Grav. 11 (1994) 689–693. [807] M. Rogatko, Class. Quant. Grav. 12 (1995) 3115–3118. [808] M. Rogatko, Phys. Rev. D58 (1998) 044011. [809] M. Rogatko, Class. Quant. Grav. 19 (2002) 875. [810] L. J. Romans, Phys. Lett. B169 (1986) 374. [811] L. J. Romans, Nucl. Phys. B383 (1992) 395–415. [812] I. Robinson, Bull. Acad. Polon. Sci. 7 (1959) 351. [813] L. Rosenfeld, Mém. Acad. Roy. Belgique 6 (1930) 30. [814] R. Ruffini and J. A. Wheeler, Physi Today, 24 (1971) 30–36. [815] H. Rumpf, Z. Naturforsch. 33a (1978) 1224–1225. [816] H. Rumpf, Gen. Relativ. Gravit. 14 (1982) 873. [817] V. de Sabbata and C. Sivaram, Spin and Torsion in Gravitation, Singapore: World Scientific (1994). [818] V. de Sabbata and M. Gasperini, Introduction to Gravitation, Singapore: World Scientific (1985). [819] N. Sakai and I. Senda, Prog. Theor. Phys. 75 (1986) 692. Erratum Prog. Theor. Phys. 77 (1987) 773. [820] J. H. Schwarz, Nucl. Phys. B226 (1983) 269–288. [821] J. H. Schwarz, in Rome String Theory Workshop (1992), pp. 503–520. [822] J. H. Schwarz, Phys. Lett. B360 (1995) 13–18. Erratum Phys. Lett. B364 (1995) 252. [823] J. H. Schwarz and P. C. West, Phys. Lett. B126 (1983) 301. [824] J. Schwinger, Phys. Rev. 82 (1951) 664–679. [825] J. Schwinger, Phys. Rev. 144 (1966) 1087. [826] J. Schwinger, Phys. Rev. 173 (1968) 1536. [827] A. Sagnotti, in Nonperturbative Quantum Field Theory, Eds. G. ’t Hooft, A. Jaffe, G. Mack, P. K. Mitter, and R. Stora, New York: Plenum Press (1988), pp. 521–528. [828] Supergravities in Diverse Dimensions, volumes 1 and 2, Eds. A. Salam and E. Sezgin, Amsterdam/Singapore: North Holland/World Scientific (1989). [829] A. Salam and J. Strathdee, Ann. Phys. (NY) 141 (1982) 316. [830] R. Schoen and S. -T. Yau, Commun. Math. Phys. 65 (1979) 45–76. [831] J. H. Schwarz, Phys. Rep. 89 (1982) 223–322. [832] J. Scherk, Rev. Mod. Phys. 47 (1975) 123–164. [833] J. Scherk and J. H. Schwarz, Nucl. Phys. B81 (1974) 118. [834] J. Scherk and J. H. Schwarz, Phys. Lett. B52 (1974) 347. [835] J. Scherk and J. H. Schwarz, Phys. Lett. 82B (1979) 60. [836] J. Scherk and J. H. Schwarz, Nucl. Phys. B153 (1979) 61–88. [837] E. Schrödinger, Proc. Roy Irish Acad. 51A (1947) 163. [838] E. Schrödinger, Space-Time Structure, Cambridge: Cambridge University Press (1954). [839] E. Schrödinger, Phys. Z. 19 (1918) 4. [840] K. Schwarzschild, Sitzungsber. deutsch. Akad. Wiss. Berlin, Kl. Math. Phys. Technik (1916) 189–196.
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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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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 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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