0035-001X

S0035-001X2007000800012

México

00 02 2007

53 85 102

An introduction to the brane world

A. Pérez–Lorenzana

Departamento de Física, Centro de Investigación y de Estudios Avanzados del I.P.N., Apartado Postal 14–740, 07000, México, D.F., México

Recibido el 18 de julio de 2005
Aceptado el 14 de marzo de 2005

Abstract

]]> The study of the so called brane world models has introduced completely new ways of looking at standard problems in many areas of theoretical physics. Inspired in the recent developments of string theory, the Brane World picture involves the introduction of new extra dimensions beyond the four we see, which could either be compact or even open (infinite). The sole existence of those new dimensions may have non–trivial observable effects in short distance gravity experiments, as well as in our understanding of the cosmology of the early Universe, among many other issues. The goal of the present notes is to provide a short introduction to Brane World models, to their motivations and consequences. We cover some of their basic aspects. The discussion includes models with flat compact extra dimensions, as well as the so–called Randall–Sundrum models.

Keywords: Brane world; extra dimensions; Randall–Sundrum models.

Resumen

En años recientes, el avance en el estudio de los llamados Mundos Brana ha provisto de nuevas formas de mirar viejos problemas de la física teórica. Los modelos de mundo brana se inspiran en desarrollos recientes de la teoría de cuerdas (la teoría de branas), y suponen la existencia de nuevas dimensiones espaciales más allá de las cuatro que vemos cotidianamente, las cuales pueden ser tanto compactas como infinitas. La existencia de dimensiones extras podría ser identificable en el comportamiento de la interacción gravitacional a pequeñas distancias. Su presencia puede, además, impactar de manera importante nuestra actual comprensión del Universo temprano y su cosmología, entre otras cosas. A lo largo de las presentes notas, cuyo interés es servir como una introducción breve al estudio de los mundos brana, revisamos algunos aspectos de estos modelos. Se discuten tanto los modelos con dimensiones extra planas y compactas, como los llamados modelos de Randall– Sundrum.

Descriptores: Mundos Brana; dimensiones extra; cosmología.

PACS: 04.50.+h;98.80.–k; 11.10.Kk

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References

1. Th. Kaluza, Sitzungober. Preuss. Akad. Wiss. Berlin (1921) 966; [ Links ] O. Klein, Z. Phys. 37 (1926) 895. [ Links ]

2. N. Arkani–Hamed, S. Dimopoulos, and G. Dvali, Phys. Lett. B 429 (1998) 263; [ Links ] I. Antoniadis et al., Phys. Lett.B 436 (1998) 257; [ Links ] I. Antoniadis, S. Dimopoulos, G. Dvali, Nucl. Phys. B 516 (1998)70. [ Links ]

3. J.C. Long, H.W. Chan, and J.C. Price, Nucl. Phys. B 539 (1999) 23; [ Links ] E.G. Adelberger et al., hep–ex/0202008; [ Links ] Hoyle et al., Phys. Rev. Lett. 86 (2001) 1418; [ Links ] J.C. Long et al., Nature 421 (2003) 27. [ Links ]

4. G. Giudice, R. Rattazzi, and J. Wells, Nucl. Phys. B 544 (1999) 3; [ Links ] T. Han, J. Lykken, and R.J. Zhang, Phys. Rev. D 59 (1999) 105006. [ Links ]

5. See for instance: E. Mirabelli, M. Perelstein, and M. Peskin, Phys. Rev. Lett. 82 (1999) 2236; [ Links ] S. Nussinov and R. Shrock, Phys. Rev. D 59 (1999) 105002; [ Links ] C. Balasz et al., Phys. Rev. Lett. 83 (1999) 2112; [ Links ] J.L. Hewett, Phys. Rev. Lett. 82 (1999) 4765; [ Links ] P. Mathew, K. Sridhar, and S. Raichoudhuri,Phys. Lett. B 450S (1999) 343; [ Links ] T.G. Rizzo, Phys. Rev. D 59 (1999) 115010; [ Links ] K. Aghase and N.G. Deshpande, Phys. Lett. B 456 (1999) 60; [ Links ] K. Cheung and W.Y. Keung, Phys. Rev. D 60 (1999) 112003; [ Links ] L3 Coll. Phys. Lett. B464 (1999) 135. [ Links ]

6. N. Arkani–Hamed, S. Dimopoulos, and G. Dvali, Phys. Rev. D 59 (1999) 086004; [ Links ] V. Barger et al., Phys. Lett. B 461 (1999) 34; [ Links ] L.J. Hall and D. Smith. Phys. Rev. D 60 (1999) 085008; [ Links ] S. Cullen and M. Perelstein, Phys. Rev. Lett. 83 (1999) 268; [ Links ] C. Hanhart et al., Nucl. Phys. B 595 (2001) 335. [ Links ]

7. See for instance: P. Nath and M. Yamaguchi, Phys. Rev. D 60 (1999) 116004; [ Links ]idem 116006; [ Links ] P. Nath, Y. Yamada, and M. Yamaguchi, Phys. Lett. B 466 (1999) 100; [ Links ] R. Casalbuoni et al. Phys. Lett. B 462 (1999) 48; [ Links ] M. Masip and A. Pomarol, Phys. Rev. D 60 (1999) 096005; [ Links ] W.J. Marciano, Phys. Rev. D 60 (1999) 093006; [ Links ] I. Antoniadis, K. Benakli, and M. Quiros, Phys. Lett. B 460 (1999) 176; [ Links ] M.L. Graesser, Phys. Rev. D 61 (2000) 074019; [ Links ] T.G. Rizzo and J.D. Wells, Phys. Rev. D 61 (2000) 016007. [ Links ]

8. E. Witten, Nucl Phys. B 471 (1996) 135; [ Links ] P. Horava and E. Witten, Nucl. Phys. B 460 (1996) 506; [ Links ]idem B 475 (1996) 94. [ Links ]

9. V.A. Rubakov and M.E. Shaposhnikov, Phys. Lett. B 152 (1983) 136; [ Links ] K. Akama, in Lecture Notes in Physics, 176, Gauge Theory and Gravitation, Proceedings of the International Symposium on Gauge Theory and Gravitation, Nara, Japan, August 20–24, (1982), edited by K. Kikkawa, N. Nakanishi, and H. Nariai, (Springer–Verlag, 1983), 267; [ Links ] M. Visser, Phys. Lett B 159 (1985) 22; [ Links ] E.J. Squires, Phys. Lett B 167 (1986) 286; [ Links ] G.W. Gibbons and D.L. Wiltshire, Nucl. Phys. B 287 (1987) 717. [ Links ]

10. I. Antoniadis, Phys. Lett. B 246 (1990) 377; [ Links ] I. Antoniadis, K. Benakli, and M. Quirós, Phys. Lett. B 331 (1994) 313. [ Links ]

11. J. Lykken, Phys. Rev. D 54 (1996) 3693. [ Links ]

12. For a review see J. Polchinski, hep–th/9611050. [ Links ]

13. G. Gogberashvili, Int. J. of Mod. Phys. D 11 1635 (2002) (hep–ph/9812296). [ Links ]

14. L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999) 3370. [ Links ]

15. L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999) 4690. [ Links ]

16. N. Arkani–Hamed et al., Phys. Rev. Lett. 84 (2000) 586. [ Links ]

17. A. Perez–Lorenzana, 9th Mexican School on Particles and Fields, Metepec, Puebla, Mexico, 2000; [ Links ] AIP Conf. Proc. 562 (2001) 53–85 [hep–ph/0008333]; [ Links ] V.A. Rubakov, Phys. Usp. 44 (2001) 871 (hep–ph/0104152); [ Links ] C. Csaki, hep–ph/0404096; [ Links ] P. Brax and C. van de Bruck, Class. Quant. Grav. 20 (2003) R201. [ Links ]

18. G. Giudice, R. Rattazzi, and J. Wells, Nucl. Phys. B 544 (1999) 3. [ Links ]

19. T. Han, J. Lykken, and R.J. Zhang, Phys. Rev. D 59 (1999) 105006. [ Links ]

20. L. Amendola, E.W. Kolb, M. Litterio, and F. Occhionero, Phys. Rev. D 42 (1990) 1944. [ Links ]

21. S. Tsujikawa, JHEP 0007 (2000) 024. [ Links ]

22. D.H. Lyth, Phys. Lett. B 448 (1999) 191; [ Links ] N. Kaloper and A. Linde, Phys. Rev. D 59 (1999) 101303. [ Links ]

23. A. Linde, Phys. Lett. B 129 (1983) 177. [ Links ]

24. A. Linde, Phys. Lett. B 259 (1991) 38; [ Links ]Phys. Rev. D 49 (1994) 748. [ Links ]

25. R.N. Mohapatra, A. Pérez–Lorenzana, and C.A. de S. Pires, Phys. Rev. D 62 (2000) 105030. [ Links ]

26. A. Mazumdar and A. Pérez–Lorenzana, Phys. Lett. B 508 (2001) 340. [ Links ]

27. A.M. Green and A. Mazumdar, Phys. Rev. D 65 (2002) 105022. [ Links ]

28. N. Arkani–Hamed et al., Nucl. Phys. B 567 (2000) 189. [ Links ]

29. G. Dvali and S.H.H. Tye, Phys. Lett. B 450 (1999) 72. [ Links ]

30. A. Mazumdar and A. Perez–Lorenzana, Phys. Rev. D 65 (2002) 107301. [ Links ]

31. E.W. Kolb, G. Servant, and T.M.P Tait, JCAP 0307 (2003) 008. [ Links ]

32. A. Mazumdar, R.N. Mohapatra, and A. Perez–Lorenzana, JCAP 0406 (2004) 004. [ Links ]

33. W.D. Goldberger and M.B. Wise, Phys. Rev. D 60 (1999) 107505. [ Links ]

34. S.L. Dubovsky, V.A. Rubakov, and P.G. Tinyakov, Phys. Rev. D 62 (2000) 105011. [ Links ]

35. C. Csaki, M.L. Greasser, L. Randall, and J. Terning, Phys. Rev. D62 (2000) 045015; [ Links ] W.D. Goldberger and M.B. Wise, Phys. Lett. B 475 (2000) 275; [ Links ] C. Charmousis, R. Gregory, and V.A. Rubakov, Phys. Rev. D 62 067505. [ Links ]

36. C. Csaki, J. Erlich, C, Grogjean, and T.J. Hollowood, Nucl. Phys. B 584 (2000) 359; [ Links ] C. Csaki, M.L. Greasser, and G.D. Kribs, Phys. Rev. D 63 (2000) 065002. [ Links ]

37. For a review see for instance E.T. Akhmedov hep–th/9911095. [ Links ]

38. W. Muck, K.S. Viswanathan, and I.V. Volovich, Phys. Rev. D 62 (2000) 105019; [ Links ] R. Gregory, V.A. Rubakov, and P.G. Tinyakov, Phys. Rev. D 62 (2000) 105011. [ Links ]

39. P. Binetruy, C. Deffayet, and D. Langlois, Nucl. Phys. B 565 (2000) 269. [ Links ]

40. P. Binetruy, C. Deffayet, U. Ellwanger, and D. Langlois, Phys. Lett. B477 (2000) 285; [ Links ] E.E. Flanagan, S.–H.H. Tye and I. Wasserman,Phys. Rev. D 62 (2000) 024011. [ Links ]

41. A. Lukas, B.A. Ovrut, and D. Waldram, Phys. Rev. D 60 (1999) 086001; [ Links ]61 (2000) 023506. [ Links ]

42. C. Csaki, M. Graesser, C. Kolda, and J. Terning, Nucl. Phys. Proc. Suppl. 79 (1999) 169; [ Links ] J.M. Cline, C. Grojean, and G. Servant, Phys. Rev. Lett. 83 (1999) 4245. [ Links ]

43. R.N. Mohapatra, A. Perez–Lorenzana, and C.A. de S. Pires, Int. J. of Mod. Phys. (2001). [ Links ]

44. T. Shiromizu, K. Maeda, and M. Sasaki, Phys. Rev. D 62 (2000) 024012. [ Links ]

45. R. Martens, D. Wands, B.A. Basset, and I.P.C. Heard, Phys. Rev. D 62 (2000) 041301. [ Links ]

46. E.J. Copeland, A.R. Liddle, and J. E. Lidsey, Phys. Rev. D 64 (2001) 023509. [ Links ]

47. R. Allahverdi, A. Mazumdar, and A. Pérez–Lorenzana, Phys. Lett. B 516 (2001) 431. [ Links ]

48. N. Arkani–Hamed, S. Dimopoulos, N. Kaloper, and R. Sundrum, Phys. Lett. B 480 (2000) 193; [ Links ] S. Kachru, M.B. Schulz, and E. Silverstein, Phys. Rev. D 62 (2000) 045021; [ Links ] S. Forste, Z. Lalak, S. Lavignac, and H.P Nilles, Phys. Lett. B 481 (2000) 360; [ Links ] C. Csaki, J. Erlich, C. Grojean, and T.J. Hollowood, Nucl. Phys. B 584 (2000) 359; [ Links ] C. Csaki, J. Erlich, and C. Grojean, Nucl. Phys. B 604 (2001) 312. [ Links ]

49. A.G. Cohen and D.B. Kaplan, Phys. Lett. B 470 (1999) 52; [ Links ] T. Gherghetta and M.E. Shaposhnikov, Phys. Rev. Lett. 85 (2000) 240; [ Links ] A. Chodos and E. Poppitz, Phys. Lett. B 471 (1999) 119. [ Links ]

50. G. Servant and T.M.P Tait, Nucl. Phys. B 650 (2003) 391; [ Links ] New J. Phys. 4 (2002) 99; [ Links ] H.C. Cheng, J.L. Feng, and K.T. Matchev, Phys. Rev. Lett. 89 (2002) 211301; [ Links ] D. Hooper and G.D. Kribs, Phys. Rev. D 67 (2003) 055003. [ Links ]

51. S.B. Giddings, E. Katz, and L. Randall, J. High Energy Phys. 03 (2000) 023; [ Links ] S.B. Giddings and S. Thomas, Phys. Rev. D 65 (2002) 056010. [ Links ]

52. A. Chamblin, S.W. Hawking, and H.S. Reall, Phys. Rev. D 61 (2000) 065007; [ Links ] J. Garriga and M. Sasaki, Phys. Rev. D 62 (2000) 043523; [ Links ] R. Emparan, G.T. Horowitz, and R.C. Myers, JHEP 0001 (2000) 007; [ Links ] R. Emparan, G.T. Horowitz, and R.C. Myers, Phys. Rev. Lett. 85 (2000) 499; [ Links ] A. Chamblin, C. Csaki, J. Erlich, and T.J. Hollowood, Phys. Rev. D 62 (2000) 044012. [ Links ]

53. N. Arkani–Hamed, A.G. Cohen, and H. Georgi, Phys. Rev. Lett. 86 (2001) 4757; [ Links ] C.T. Hill, S. Pokorski, and J. Wang, Phys. Rev. D 64 (2001) 105005. [ Links ] ]]> 1 1921 966 1926 37 37 895 2 1998 429 429 263 1998 436 436 257 1998 516 516 70 3 1999 539 539 23 2001 86 86 2003 421 421 27 4 1999 544 544 3 1999 59 59 105006 5 1999 82 82 2236 1999 59 59 105002 1999 83 83 2112 1999 82 82 4765 1999 450S 450S 343 1999 59 59 115010 1999 456 456 60 1999 60 60 112003 1999 B464 B464 135 6 1999 59 59 086004 1999 461 461 34 1999 60 60 085008 1999 83 83 268 2001 595 595 335 7 1999 60 60 116004 116006 1999 466 466 100 1999 462 462 48 1999 60 60 096005 1999 60 60 093006 1999 460 460 176 2000 61 61 074019 2000 61 61 016007 8 1996 471 471 135 1996 460 460 506 1996 475 475 94 9 1983 152 152 136 1982 Nara 267 1985 159 159 22 1986 167 167 286 1987 287 287 717 10 1990 246 246 377 1994 331 331 313 11 1996 54 54 3693 12 13 2002 11 1635 1635 14 1999 83 83 3370 15 1999 83 83 4690 16 2000 84 84 586 17 2000 Metepec Puebla 2001 562 562 53-85 2001 44 44 871 2003 20 20 R201 18 1999 544 544 3 19 1999 59 59 105006 20 1990 42 42 1944 21 2000 0007 0007 024 22 1999 448 448 191 1999 59 59 101303 23 1983 129 129 177 24 1991 259 259 38 1994 49 49 748 25 2000 62 62 105030 26 2001 508 508 340 27 2002 65 65 105022 28 2000 567 567 189 29 1999 450 450 72 30 2002 65 65 107301 31 2003 0307 0307 008 32 2004 0406 0406 004 33 1999 60 60 107505 34 2000 62 62 105011 2000 D62 D62 045015 2000 475 475 275 62 62 067505 36 2000 584 584 359 2000 63 63 065002 37 38 2000 62 62 105019 2000 62 62 105011 39 2000 565 565 269 40 2000 B477 B477 285 2000 62 62 024011 41 1999 60 60 086001 2000 61 61 023506 42 1999 ^s79 ^s79 79 169 1999 83 83 4245 43 2001 44 2000 62 62 024012 45 2000 62 62 041301 46 2001 64 64 023509 47 2001 516 516 431 48 2000 480 480 193 2000 62 62 045021 2000 481 481 360 2000 584 584 359 2001 604 604 312 49 1999 470 470 52 2000 85 85 240 1999 471 471 119 50 2003 650 650 391 2002 4 4 99 2002 89 89 211301 2003 67 67 055003 51 2000 03 03 023 2002 65 65 056010 52 2000 61 61 065007 2000 62 62 043523 2000 0001 0001 007 2000 85 85 499 2000 62 62 044012 53 2001 86 86 4757 2001 64 64 105005