Gravity and Strings

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M2 M5 d = 11 KK7 KK9 WM D8 D6 D2 D4 D0 IIA KK9A KK8A S5A KK6A KK7A F1A WA d = 10 IIB D-1 WB D1 F1B D3 S5B D5 KK6B D7 S7 D9 S9 T Duality Identical Solutions E-M Duality Direct Dimensional Reduction Double Dimensional Reduction Fig. 19.5. Duality relations between classical solutions of ten- <strong>and</strong> 11-dimensional supergravity theories: p-branes, M-branes, D-branes, waves, <strong>and</strong> Kaluza–Klein monopoles. Lines with two arrows denote T-duality relations; dashed lines denote S-duality relations. Lines with a single arrow denote relations of dimensional reduction, either vertical (direct dimensional reduction) or diagonal (double dimensional reduction). Pairs of branes in boxes are type-IIB S-duality doublets.
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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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524 The extended objects of string
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Page 1150: 19.4 Duality of string-theory solut
Page 1154: 19.5 String-theory extended objects
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Page 1174: 19.6 Intersections 567 outside the
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Page 1182: 19.6 Intersections 571 The coordina
Page 1186: 20 String black holes in four and f
Page 1190: 20.1 Composite dilaton black holes
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20.2 Black holes from branes 577 If
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20.2 Black holes from branes 579 si
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20.2 Black holes from branes 581 Th
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20.2 Black holes from branes 583 Th
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20.2 Black holes from branes 585 (y
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20.2 Black holes from branes 587 wh
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20.3 Entropy from microstate counti
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Appendix A Lie groups, symmetric sp
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Lie groups, symmetric spaces, and Y
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G/H isreductive if Lie groups, symm
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Appendix B Gamma matrices and spino
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Gamma matrices and spinors 613 wher
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Gamma matrices and spinors 615 or,
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Gamma matrices and spinors 617 Usin
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For instance, we can obtain Gamma m
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Gamma matrices and spinors 621 It i
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Gamma matrices and spinors 623 We w
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Gamma matrices and spinors 625 and,
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Gamma matrices and spinors 627 Thus
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Gamma matrices and spinors 629 Tabl
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Gamma matrices and spinors 631 Thes
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Gamma matrices and spinors 633 labe
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Appendix C 635 For some purposes, s
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Appendix C 637 C.2 Squashed S 3 and
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Appendix E Conformal rescalings If
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Connections and curvature component
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and the Ricci scalar is given by We
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Connections and curvature component
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The Ricci scalar is Connections and
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The harmonic operator on R 3 × S 1
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[35] E. Álvarez, L. Álvarez-Gaum
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[128] E. Bergshoeff, R. Kallosh, T.
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[222] L. Castellani, R. D’Auria,
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[316] S. Deser and B. Zumino, Phys.
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[411] D. V. Gal’tsov and O. V. Ke
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[506] S. F. Hassan, Nucl. Phys. B58
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References 663 [600] J. M. Izquierd
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[696] R. R. Metsaev and A. A. Tseyt
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[793] H. Quevedo, Fortschr. Phys. 3
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[889] G. ’t Hooft, Nucl. Phys. B6
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Index Page numbers in italic are th
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isotropic, 198, 216, 232, 234, 265,
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Noether method, 78 first-order form
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integrability equation in N = 2, d
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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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Gravity and Strings

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