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Harv Lett. , at anes, ef blac solution. . se (2000) v J. localized y Langlois, vity (1999) orld (1926) (Math. dimensions, Re 4D . unresolv Planck D-br 1987). a 285 dimensions D. theories, ed. Kaluza-Klein anes, gra (W (2000) with , , , ys. of 895 on xtr br 4690 Katherine the alid , e 99 , ark, and Ramond-Ramond Ph Berlin v Dimopoulos 477 es 1987). P hierarch on at dimensions 37 field of ane-univer 83 scale ersality B S. w e ASI v es br iss. and Modern 023506 v ys. T ark, Theories ne a , anger Randall-Sundrum W P Efthimiou in Lectur uni Lett. Ph dimension w Lett. Menlo induce 61 . esence J. , dimension a anes om v fecti the and Planck Lectur Z. alidated ge y Ell sub-millimeter D pr fr Notes ys. dimension, , v ef . xtr in Re f, originates Akad. e v e a U. Menlo Ph gy xtra esle the RS and char , e with which ys. Re 4D xtr y Duf hlet-Br oblem e in vity one Greene, translation [hep-ph/9807344]. J. an Ph Polchinski, pr ayet, Arkani-Hamed, ys. Lectur Kaluza-Klein f of esle eting gra Preuss. Relativity J. B. weak Diric M. Ph . xpansion hy N. cosmolo matter gy e c small Def rigorously constant, Of theories when a models, ar and (1999) see avity: and English C. (Addison-W of xpansion , , e and Modern Gr gical om scale in hier gical Reinterpr gy fr well-defined in [hep-th/9912164]. inflation, Theory Cosmolo (Addison-W ventional matter Efthimiou, 10 defect eV matter and theory hy [hep-ph/9910498]. Polchinski, The gical Sitzungsber 086004 / T Freund c , J. C. M Binetruy compactification, ar 5D G. ali, 2000) Cosmolo . cosmolo yields 4D cosmolo anes scale reprinted . P 013 Models: to D59 erning, see P [hep-th/9510017]; Freund ed. and dimension Dv hier . Br (2000) , T Non-con , [hep-ph/9803315]; v translation Boundary eV Cosmolo Physics, and with G. J. G. T and apore, well, electromagnetic . Re vity unified [hep-th/9611050]. xtra In [hep-ph/9906513]. P mass e ulk ant, theory (1995) induces and (1986)]; 4D as b and e ys. gra asserman, duality Sing (1998) 044039 g ive-Dimensional Strings, [hep-ph/9906523]. a and , aldram, English W alternative F Ph Langlois, xtradimensional eV Serv Unity in , 241 lar ophysics and in e Chodos olda I. W T (1999) 62 4724 and in , adimensional small , 263 super string . An case, instead, A D. K , 293-356 5 G. a solution, , Of And D . D. astr 34 in in . F avity A. 75 y and vity (1999) , , at Extr v [hep-th/9905012]; ys. Chodos and ably space and gr arped gy . C. Scientific, This ye and B429 Re gra strings Ph 1997) , Dimopoulos 462 volution T w oblem Lett. e A. 4245 reprinted Theory g. ayet branes B . branes scale S. ys. , Pr arped f H. orld v Sundrum, Sundrum, Sitter (2000) Lett. W hierarch to of 83 scale Ovrut ields, Ph arps. S. Re (W R. R. Grojean apore, Def ulk Ener gical F unresolv The quantum in background, w w Lett. ys. Appelquist, b 269 Graesser A. [hep-ph/9905221]. . specific C. an, 1 ys. C. , (1921); . Ph and Lett. and , On ys. − Sing Pl B. anti-de , T . M. Quantum Phenomenolo Ph ervie High with avity v scale , 1996, Planck 565 M v Ph Appelquist, 966 alidated Kachru o , . cosmolo ys scenario, , v Gr es, Re B ali, and Cline, (1999) . Flanag eV e unified g 12 4D T T S. introduction an a Dv Klein, Arkani-Hamed, Lukas, Csaki, Randall E. Randall ys. ys. Kaluza, ane Binetruy M. avity and ences 1921 or or . described . [Surv Theories ) Boulder Char Scientific, ed. [hep-th/9902071]. gr world and holes [hep-th/9910219]; and [hep-th/9906064]. Ph Ph theories G. 3370 Br millimeter O. T F F C. L. L. N. P E. A. J. size I them y [1] [2] [3] [4] [9] [6] [7] [5] [8] In field rigorously tin Refer inducing Randall-Sundrum Matter [11] [12] [10] PoS(jhw2004)013 , , B , , 042 153 66 62 D , Lett. 68 , ys. 63 . D (1989). v Benson D Suppl. D 4922 a . ys. . D Ph . , 486 v v . v Re 0202 solutions xtr by ys. v Ph 83 391 B e the Re warped (2004) Re , Re , e ys. Ph Re in g . in Nucl. gical ys. dimensions, gical ys. Ph ys. JHEP 316 058 Lett. Lett. ys. -qc/0112027]. , lar a , Katherine , . space Ph Ph B Ph v se inflation , Ph gy anes , [gr xtr ys. [hep-th/0404116]. on [hep-th/0303194]. Theor , scalar e Re br ys. Ph 0408 es cosmolo ane , owski ane Cosmolo Ph ulk ys. br univer b world [hep-th/0307049]. theory Prog. br the dimensions, (2002) (2004) Ph (2003) cosmolo A orbifolds, vis, avity lectur the JHEP Mink I ane the Opaque Nucl. gr and ven early on Da br , 072 , 046 on string 5D , (2004) , on RS noncompact se ele fields, C. [astro-ph/0006421]. ICTP the in 104020 gas in Sasaki, [hep-th/0011045]. anes oduction, , agner A. in 060 om ulk 0405 0305 br with , b 65 M. fr W eting Ending ane intr localized Univer inflation D landscape?, and inflaton vacua string (2001) br E. . An (2001) and gases v a 0401 with JHEP JHEP C. with oblem Re [hep-th/0302219]. on Early Gabadadze, Brax gy: gical pr Sitter Randall-Sundrum 289 , ane . theory Reinterpr self-tuned , and dynamics P inflation: Chaotic without anaka ys. 023509 G. JHEP to Br hy De T , The 11 vacua, c vacua, on theory ait avity . Ph in 497 / T T 64 ar In theory gr [hep-ph/0212307]. string B w cosmolo edi, Steep string flux D Cosmolo v , stabilization Heard, a M. I vacua, . 013 Models: hier y ections vie ri 4D of . v e inflation Easson, theory I. T ane T re Lett. string . volution Re strings M the flux D. P e type (2003) Br corr ther / of and dynamics, Lidse see ys. S. ys. Is utions Jackson, Himemoto, and E. Modulus , Porrati, and Ph . Super v Ph gical Ponton, [hep-th/0104023]; J. Y G. and string five-dimensional ane-world Solving a, ger M. rho**2 096006 ise, otic E. Bassett a , af Counting inflaton of adimensional Br M. Langlois, Distrib W and V [hep-th/9910132]. landscape in 67 der and A. spaces, 4d D. Linde B. Gorbato (2001) C. Extr and Heter D Cosmolo Or B. oduction, . in Kaplan, E. A. the v opic M. Carena, pr Liddle Sasaki, 007 and (1999) vis, B. Douglas, , statistics Brandenber Re bosons inet, Douglas, itten, [hep-th/0005212]. and wed [hep-th/0005016]; arped M. R. ands, and e M. -qc/0010035]; singular V Da 52 ger R. D. anthr Greene W H. W R. , [hep-th/9510209]; [hep-th/0209261]. ys. W mimic in vie J. The A. Gabadadze in 0105 [hep-ph/9912464]. [hep-th/0204099]. [hep-th/0301240]. [gr C. ger in R. E. Kallosh, R. re and M. Ph w particle Dine D. M. and The , Gaug G. hep-ph/0308112. can A. (2000) and (2000) B. B470 R. vie , and avity M. and (1996) (2003) and JHEP re avity ali, a (2000) (2002) (2003) (2001) gr and nicely v 208 [hep-th/0201041]. [hep-ph/9911294]. [hep-ph/9907447]. ounds, Goldber Douglas, Gr xander Cohen Lett. , Dv Brandenber world Cline is 506 181 Copeland, nice 103509 , , kgr R. D. G. R. Pomarol, Maartens, Easther H. J. Susskind, Himemoto Ale Ashok Kachru, ys. Banks, super , Denef Brax Hora 485 M. avitational ane . and . . . . . constant, (2002) 041301 62 of gr [hep-th/0309170]. Ph 023502 046005 044015 br bac 460 (2000) 148 dimensions, B (1999) J. P E. R. S. R. R. T F M. S. A. Y L. This S. See G. W P A. Matter [13] [14] [16] [30] [31] [15] [32] [28] [29] [26] [27] [33] [17] [25] [18] [24] [22] [19] [20] [23] [21] PoS(jhw2004)013 s six [Usp. 136 The in ys. , (2003) 64 Benson o x 044014 , T the Ph higher , scalar 21 125 , in 62 396 oblem?, (2001) B vorte and preparation. 20 B D mass with dimensions, pr . . v in hep-th/0405144. v 871 two -dimensional Solution Katherine Lett. six (2000) , Re Lett. Gra A in (2001) 44 stable solutions dimensions, Abelian ys. ound, ds ys. ys. [hep-th/0309259]. to constant 2564 Ph se (2000) Higher on , dimension h vortices, Ph Ph kgr Usp. Quant. defect g: 84 world owar 065026 113 e T oac bac all?, gical ys. fifth , , (2003) codimension ansver eho W ane model Ph tr Lett. in the appr defects, Class. 496 RS br . D64 theories, gs 040 v . string hedg w B x, , v two a cosmolo Re string-lik ne Hig Re in eting Domain a A global [hep-th/0006251]. defects vorte 0311 the Lett. ys. compactification A oduction, warped Dimensions: e global ces on and coupled Modeling Ph inside w ys. (1983). Phys. intr , ime ne solve sour Ph JHEP world: (2000) global arped avity Inside , An Reinterpr 139 ongly W , [hep-th/0012033]. gr warped se Karch, Living , string-lik 12 the ane str anes 353 , v a some / Live v o , A. 125 -dimensional of br Space-T defect, in o on in e xtended e monopole On p-br e a [hep-th/9909134]. B e W univer 491 , (2001) 013 Models: [hep-th/0104118]. and v [hep-th/0008087]. e B [hep-th/9612128]. o [hep-th/0012165]. walls Extr Do higher and compactifications Lett. Localizing dimensions: , , 042 -lik s compactifications, v v , physics global of , a (2000) Global structur v o o Lett. a Shaposhnik ys. o (2001) string-lik Gubser (2000) Shaposhnik xtr localization (2001) gular a cigar e in (1997)] Ph E. ys. 0102 factor S. avity E. Domain string Kim, world A 615 Re [hep-th/0004014]. se on 329 , Ph Shaposhnik S. M. Gr 467 , 046008 s adimensional codimension-two 452 , B. M. avity arp , ane , , . [hep-ph/0104152]. E. W JHEP 619 Spacetime infinite Y oblem, Gr Br 491 62 and Shaposhnik Shaposhnik , global Extr 602 univer and Can Shaposhnik avity B 407 (2000) [hep-th/9909199]. Pr M. B D matter E. E. Moreno, A B Moreno, Shifman, gr . and and B yer ilenkin, E. v ys. of e y V 240 and (2001)] A. M. M. M. M. ys. g Freedman, Santos, oebbe, , Me arped Re Ph Lett. M. Poppitz, Cline, Re Roessl T Poppitz, Cho, A. J. J. W (1999) Ph 85 M. Z. C. H. Lar J. E. 913 J. I. and and ys. ys. E. E. M. , in Constant and , localize espondence v v v D. and and and S. 119 Ph Nucl. Ph J. Nonsingular o o o and and -Daemi and , , and and Lett. , Nucl. 171 and corr . that , avity asti ali gical v annini, and olfe, 471 ghetta ghetta, Localization [hep-th/0003300]. [Erratum-ibid. hy v gory gory avity Gr c Re Dv Carlos Carlos Rubak Rubak Rubak Moon, B Nauk gr ar inet Gio Chodos Benson DeW Benson R. Gre de Gre de Ponton A. A. A. Randjbar H. ys. Gher Gher V Olasag Oda, and . . . . . AdS/CFT Lett. Ph dimensions, [hep-th/9911015]. [hep-th/0208037]. (2000) Cosmolo (1983). (1997) and [hep-th/0104067]. dimensions, hep-th/0406141. [hep-th/0006203]. hier solutions Fiz. A. M. R. E. I. T B. R. B. K. V O. V J. V K. G. T S. S. I. Matter [34] [39] [40] [38] [35] [37] [41] [36] [42] [43] [51] [44] [53] [49] [50] [48] [52] [45] [46] [47] [54] PoS(jhw2004)013 , in Lett. B , Benson 586 ys. B models, Ph Lett. , ys. scenario, the ys. Ph monopole in Ph Katherine eometry g Nucl. global model d AdS, Randall-Sundrum of ane-worlds, compactification warped preparation. in br a standar in RS slice on om a [hep-ph/9912498]. fr Bulk theory non-factorizable in eting in models, o-modes (2000) theory fective zer ef Reinterpr Randall-Sundrum amaguchi, symmetry mixings Y 4D 13 fective the 084025 / ef and , M. ermion super and in adimensional F , 62 , 4D 013 Models: and v xtr D and o e . fields v masses sality and Re hy fields Okada c Bulk ys. warped univer ar N. [hep-ph/9907218]. e Ph Bulk ise, in g Neutrino Shaposhnik adimensional W Hier E. har c B. avity os, (1999) Extr ound, , M. Nakano, gr hy M. kgr c Pomarol, Neubert, H. and ar and [hep-ph/9912408]. arped A. bac and Domok M. 107505 W [hep-th/0008079]. , hier S. ger in and 60 and Hisano, Matter On -Daemi (2000) [hep-ph/0003129]. and D J. . (2000) avity v ghetta 361 Goldber Gr Re , 361 (2000) , D. Benson, Benson Benson, Grossman Randjbar Chang, ys. Gher 474 . and . . hep-th/0407276. Ph preparation. 492 B 141 Randall-Sundrum K. K. T W K. S. S. Y [57] [58] [60] [59] [56] Matter [55] [62] [61]