TOWARDS REALISTIC MODELS FROM HIGHER-DIMENSIONAL THEORIES WITH FUZZY EXTRA DIMENSIONS
We briefly review the Coset Space Dimensional Reduction (CSDR) programme and the best model constructed so far and then we present some details of the corresponding programme in the case that the extra dimensions are considered to be fuzzy. In particular, we present a four-dimensional N = 4 Super Yang Mills theory, orbifolded by Z3, which mimics the behaviour of a dimensionally reduced N = 1, 10-dimensional gauge theory over a set of fuzzy spheres at intermediate high scales and leads to the trinification GUT SU(3)3 at somehow lower, which in turn can be spontaneously broken to the MSSM in low scales.
Keywords: coset space dimensional reduction, unification, fuzzy spheres, orbifold projection
References:
[1] M. B. Green, J. H. Schwarz and E. Witten, Cambridge, Uk: Univ. Pr. ( 1987) 469 p. ( Cambridge Monographs On Mathematical Physics); D. Lust and S. Theisen, Lect. Notes Phys. 346 (1989) 1; J. Polchinski, Cambridge, UK: Univ. Pr. (1998) 531 p. K. Becker, M. Becker and J. H. Schwarz, Cambridge, UK: Cambridge Univ. Pr. (2007) 739 p. E. Kiritsis, Princeton University Press, 2007.
[2] A. Connes, Academic Press 1994; J. Madore, Lond. Math. Soc. Lect. Note Ser. 257, 1 (2000).
[3] N. Seiberg and E. Witten,“String theory and non commutative geometry,” JHEP 9909, 032 (1999) [arXiv:hep-th/9908142].
[4] G. Lopes Cardoso, G. Curio, G. Dall’Agata, D. Lust, P. Manousselis and G. Zoupanos, Nucl. Phys. B 652 (2003) 5 [hep-th/0211118].
[5] K. Becker, M. Becker, K. Dasgupta and P. S. Green, JHEP 0304 (2003) 007 [hep-th/0301161].
[6] K. Becker, M. Becker, P. S. Green, K. Dasgupta and E. Sharpe, Nucl. Phys. B 678 (2004) 19 [hep-th/0310058].
[7] S. Gurrieri, A. Lukas and A. Micu, Phys. Rev. D 70 (2004) 126009 [hep-th/0408121].
[8] I. Benmachiche, J. Louis and D. Martinez-Pedrera, Class. Quant. Grav. 25 (2008) 135006 [arXiv:0802.0410 [hep-th]].
[9] A. Micu, Phys. Rev. D 70 (2004) 126002 [hep-th/0409008].
[10] A. R. Frey and M. Lippert, Phys. Rev. D 72 (2005) 126001 [hep-th/0507202].
[11] P. Manousselis, N. Prezas and G. Zoupanos, Nucl. Phys. B 739 (2006) 85 [hep-th/0511122].
[12] A. Chatzistavrakidis, P. Manousselis and G. Zoupanos, Fortsch. Phys. 57 (2009) 527 [arXiv:0811.2182 [hep-th]].
[13] A. Chatzistavrakidis and G. Zoupanos, JHEP 0909 (2009) 077 [arXiv:0905.2398 [hep-th]].
[14] B. P. Dolan and R. J. Szabo, JHEP 0908 (2009) 038 [arXiv:0905.4899 [hep-th]].
[15] O. Lechtenfeld, C. Nolle and A. D. Popov, JHEP 1009 (2010) 074 [arXiv:1007.0236 [hep-th]].
[16] A. D. Popov and R. J. Szabo, JHEP 1202 (2012) 033 [arXiv:1009.3208 [hep-th]].
[17] M. Klaput, A. Lukas and C. Matti, JHEP 1109 (2011) 100 [arXiv:1107.3573 [hep-th]].
[18] A. Chatzistavrakidis, O. Lechtenfeld and A. D. Popov, JHEP 1204 (2012) 114 [arXiv:1202.1278 [hep-th]].
[19] J. Gray, M. Larfors and D. Lust, JHEP 1208 (2012) 099 [arXiv:1205.6208 [hep-th]].
[20] M. Klaput, A. Lukas, C. Matti and E. E. Svanes, JHEP 1301 (2013) 015 [arXiv:1210.5933 [hep-th]].
[21] P. Forgacs and N. S. Manton, Commun. Math. Phys. 72 (1980) 15; E. Witten, Phys. Rev. Lett. 38, 121 (1977).
[22] D. Kapetanakis and G. Zoupanos, Phys. Rept. 219 (1992) 1.
[23] Y. A. Kubyshin, I. P. Volobuev, J. M. Mourao and G. Rudolph, Lect. Notes Phys. 349 (1990) 1.
[24] J. Scherk, J. H. Schwarz, Phys.Lett. B82 (1979) 60
[25] P. Candelas, G. T. Horowitz, A. Strominger, E. Witten, Nucl. Phys. B 258, (1985) 46
[26] M. Grana, Phys. Rept. 423, 91 (2006), arXiv: 0509003[hep-th]; M.R. Douglas, S. Kachru, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102]; R. Blumenhagen, B. Kors, D. Lu¨st, S. Stieberger, Phys. Rept. 445 (2007) 1 [hep-th/0610327]; F. Denef, arXiv:0803.1194 [hep-th]
[27] Butruille J.-B., [arXiv:math.DG/0612655].
[28] N. Irges and G. Zoupanos, Phys. Lett. B698, (2011) 146 [arXiv:hep-ph/1102.2220]; N. Irges, G. Orfanidis, G. Zoupanos, arXiv:1205.0753 [hep-ph].
[29] T. Filk, Phys. Lett. B 376 (1996) 53; J. C. Varilly and J. M. Gracia-Bondia, Int. J. Mod. Phys. A 14 (1999) 1305 [hep-th/9804001]; M. Chaichian, A. Demichev and P. Presnajder, Nucl. Phys. B 567 (2000) 360 [hep-th/9812180]; S. Minwalla, M. Van Raamsdonk and N. Seiberg, JHEP 0002 (2000) 020 [hep-th/9912072].
[30] H. Grosse and R. Wulkenhaar, Lett. Math. Phys. 71 (2005) 13 [hep-th/0403232].
[31] H. Grosse and H. Steinacker, Adv. Theor. Math. Phys. 12 (2008) 605 [hep-th/0607235];H. Grosse and H. Steinacker, Nucl. Phys. B 707 (2005) 145 [hep-th/0407089].
[32] P. Aschieri, J. Madore, P. Manousselis and G. Zoupanos, JHEP 0404 (2004) 034 [hep-th/0310072]; P. Aschieri, J. Madore, P. Manousselis and G. Zoupanos, Fortsch. Phys. 52 (2004) 718 [hep-th/0401200].
[33] B. Jurco, P. Schupp, J. Wess, Nucl. Phys. B604 (2001) 148-180, [arXiv:hep-th/0102129].
[34] P. Aschieri, T. Grammatikopoulos, H. Steinacker and G. Zoupanos, JHEP 0609 (2006) 026 [hep-th/0606021].
[35] H. Steinacker and G. Zoupanos, JHEP 0709 (2007) 017 [arXiv:0706.0398 [hep-th]].
[36] A. Chatzistavrakidis, H. Steinacker and G. Zoupanos, Fortsch. Phys. 58 (2010) 537 [arXiv:0909.5559 [hep-th]].
[37] J. Maalampi and M. Roos, Phys. Rept. 186 (1990) 53.
[38] A. Chatzistavrakidis, H. Steinacker and G. Zoupanos, JHEP 1005 (2010) 100 [arXiv:1002.2606 [hep-th]].
[39] S. Heinemeyer, M. Mondragon and G. Zoupanos, Int. J. Mod. Phys. A29 (2014) 18, [hep-ph/1430032].
[40] M. Mondragon, N. Tracas and G. Zoupanos [arXiv:1403.7384 [hep-ph]].
[41] S. Heinemeyer, M. Mondragon and G. Zoupanos, SIGMA 6 (2010) 049 [arXiv:1001.0428 [hep-ph]].
[42] E. Ma, M. Mondragon and G. Zoupanos, JHEP 0412 (2004) 026 [hep-ph/0407236]; S. Heinemeyer, E. Ma, M. Mondragon and G. Zoupanos, AIP Conf. Proc. 1200 (2010) 568 [arXiv:0910.0501 [hep-ph]].
[43] N. S. Manton Nucl. Phys. B193, 502(1981).
[44] G. Chapline and R. Slansky Nucl. Phys. B204, 461(1982).
[45] C. Wetterich, Nucl. Phys. B222, 20(1985); L. Palla, Z. Phys. C24, 345(1983); K. Pilch and A. N. Schellekens, J. Math. Phys. 25, 3455(1984); P. Forgacs, Z. Horvath and L. Palla, Z. Phys. C30, 261(1986); K. J. Barnes, P. Forgacs, M. Surridge and G. Zoupanos, Z. Phys. C33, 427(1987).
[46] E. Witten, Phys. Lett. B144, 351(1984).
[47] K. Pilch and A. N. Schellekens, Nucl. Phys. B259, 673(1985); D. Luest, Nucl. Phys. B276, 220(1985); D. Kapetanakis and G. Zoupanos, Phys. Lett. B249, 66(1990).
[48] D. Lu¨st and G. Zoupanos, Phys. Lett. B165 (1985) 309; D. Kapetanakis and G. Zoupanos, Z. Phys. C56 (1992); G. Douzas, T. Grammatikopoulos and G. Zoupanos, Eur. Phys. J. C59 (2009) 917.
[49] P.Manousselis and G. Zoupanos, JHEP 0203 (2002) 002.
[50] P. Manousselis and G. Zoupanos, JHEP 0411 (2004) 025.
[51] N. Kozimirov, V. A. Kuzmin and I. I. Tkachev, Sov. J. Nucl. Phys. 49, 164(1989); D. Kapetanakis and G. Zoupanos, Phys. Lett. B232, 104(1989).
[52] G. Zoupanos, Phys. Lett. B201, 301(1988).
[53] Y. Hosotani, Phys. Lett. B126, 309(1983); B129, 193(1983); E. Witten, Nucl. Phys B258, 75(1985); J. D. Breit, B. A. Ovrut and G. C. Segre, Phys. Lett. B158, 33(1985); B. Greene, K. Kirklin and P. J. Miron, Nucl. Phys. B274, 574(1986); B. Greene, K. Kirklin, P. J. Miron and G. G. Ross, Nucl. Phys. B278, 667(1986).
[54] K. S. Babu, X.-G. He and S. Pakvasa, Phys. Rev. D33 (1986) 763; G. K. Leontaris and J. Rizos, Phys. Lett. B632 (2006) 710; J. Sayre, S. Wiesenfeld and S. Willenbrock, Phys. Rev. D73 (2006) 035013.
[55] S. Kachru and E. Silverstein, Phys. Rev. Lett. 80 (1998) 4855 [hep-th/9802183].
( 623.17 kB ) 
( 513.54 kB )
Issue: 12, 2014
Series of issue: Issue 12
Pages: 85 — 93
Downloads: 598