×

Operator analysis of physical states on magnetized \(T^2 /Z_N\) orbifolds. (English) Zbl 1326.81255

Summary: We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases \(T^2 / Z_3\), \(T^2 / Z_4\) and \(T^2 / Z_6\). We can obtain the exact and analytical results which can be applicable for any larger values of the quantized magnetic flux \(M\), and show that the (non-diagonalized) kinetic terms are generated via our formalism and the number of the surviving physical states are calculable in a rigorous manner by simply following usual procedures in linear algebra in any case. Our approach is very powerful when we try to examine properties of the physical states on (complicated) magnetized orbifolds \(T^2 / Z_3\), \(T^2 / Z_4\), \(T^2 / Z_6\) (and would be in other cases on higher-dimensional torus) and could be an essential tool for actual realistic model construction based on these geometries.

MSC:

81V22 Unified quantum theories
57R18 Topology and geometry of orbifolds
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Bachas, C., A way to break supersymmetry
[2] Blumenhagen, R.; Goerlich, L.; Kors, B.; Lust, D., Noncommutative compactifications of type I strings on tori with magnetic background flux, J. High Energy Phys., 0010, 006 (2000) · Zbl 0965.81113
[3] Angelantonj, C.; Antoniadis, I.; Dudas, E.; Sagnotti, A., Type I strings on magnetized orbifolds and brane transmutation, Phys. Lett. B, 489, 223-232 (2000) · Zbl 1031.81579
[4] Blumenhagen, R.; Kors, B.; Lust, D., Type I strings with F flux and B flux, J. High Energy Phys., 0102, 030 (2001)
[5] Cremades, D.; Ibanez, L.; Marchesano, F., Computing Yukawa couplings from magnetized extra dimensions, J. High Energy Phys., 0405, 079 (2004)
[6] Blumenhagen, R.; Cvetic, M.; Langacker, P.; Shiu, G., Toward realistic intersecting D-brane models, Annu. Rev. Nucl. Part. Sci., 55, 71-139 (2005)
[7] Blumenhagen, R.; Kors, B.; Lust, D.; Stieberger, S., Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rep., 445, 1-193 (2007)
[8] Fujimoto, Y.; Nagasawa, T.; Nishiwaki, K.; Sakamoto, M., Quark mass hierarchy and mixing via geometry of extra dimension with point interactions, PTEP, Proces. Teh. Energ. Poljopr., 2013, 023B07 (2013) · Zbl 07406634
[9] Fujimoto, Y.; Nishiwaki, K.; Sakamoto, M., CP phase from twisted Higgs VEV in extra dimension, Phys. Rev. D, 88, 115007 (2013)
[10] Fujimoto, Y.; Nishiwaki, K.; Sakamoto, M.; Takahashi, R., Realization of lepton masses and mixing angles from point interactions in an extra dimension
[11] Cremades, D.; Ibanez, L.; Marchesano, F., Yukawa couplings in intersecting D-brane models, J. High Energy Phys., 0307, 038 (2003)
[12] Cvetic, M.; Papadimitriou, I., Conformal field theory couplings for intersecting D-branes on orientifolds, Phys. Rev. D, 68, 046001 (2003)
[13] Abel, S.; Owen, A., Interactions in intersecting brane models, Nucl. Phys. B, 663, 197-214 (2003) · Zbl 1059.81585
[14] Honecker, G.; Vanhoof, J., Yukawa couplings and masses of non-chiral states for the Standard Model on D6-branes on T6/Z6′, J. High Energy Phys., 1204, 085 (2012) · Zbl 1348.81371
[15] Abel, S.; Owen, A., N point amplitudes in intersecting brane models, Nucl. Phys. B, 682, 183-216 (2004) · Zbl 1045.81531
[16] Abel, S.; Goodsell, M., Intersecting brane worlds at one loop, J. High Energy Phys., 0602, 049 (2006)
[17] Abel, S.; Goodsell, M., Realistic Yukawa couplings through instantons in intersecting brane worlds, J. High Energy Phys., 0710, 034 (2007)
[18] Pesando, I., Green functions and twist correlators for \(N\) branes at angles, Nucl. Phys. B, 866, 87-123 (2013) · Zbl 1262.81148
[19] Pesando, I., Correlators of arbitrary untwisted operators and excited twist operators for \(N\) branes at angles, Nucl. Phys. B, 886, 243-287 (2014) · Zbl 1325.81147
[20] Abe, H.; Kobayashi, T.; Ohki, H.; Oikawa, A.; Sumita, K., Phenomenological aspects of 10D SYM theory with magnetized extra dimensions, Nucl. Phys. B, 870, 30-54 (2013) · Zbl 1262.81250
[21] Abe, H.; Kobayashi, T.; Sumita, K.; Tatsuta, Y., Gaussian Froggatt-Nielsen mechanism on magnetized orbifolds
[22] Abe, H.; Choi, K.-S.; Kobayashi, T.; Ohki, H., Higher order couplings in magnetized brane models, J. High Energy Phys., 0906, 080 (2009)
[23] Abe, H.; Choi, K.-S.; Kobayashi, T.; Ohki, H., Non-Abelian discrete flavor symmetries from magnetized/intersecting brane models, Nucl. Phys. B, 820, 317-333 (2009) · Zbl 1194.81178
[24] Abe, H.; Choi, K.-S.; Kobayashi, T.; Ohki, H., Magnetic flux, Wilson line and orbifold, Phys. Rev. D, 80, 126006 (2009)
[25] Abe, H.; Choi, K.-S.; Kobayashi, T.; Ohki, H., Flavor structure from magnetic fluxes and non-Abelian Wilson lines, Phys. Rev. D, 81, 126003 (2010)
[26] Berasaluce-Gonzalez, M.; Camara, P.; Marchesano, F.; Regalado, D.; Uranga, A., Non-Abelian discrete gauge symmetries in 4d string models, J. High Energy Phys., 1209, 059 (2012) · Zbl 1397.83125
[27] Honecker, G.; Staessens, W., To tilt or not to tilt: discrete gauge symmetries in global intersecting D-brane models, J. High Energy Phys., 1310, 146 (2013)
[28] Marchesano, F.; Regalado, D.; Vazquez-Mercado, L., Discrete flavor symmetries in D-brane models, J. High Energy Phys., 1309, 028 (2013)
[29] Abe, H.; Kobayashi, T.; Ohki, H.; Sumita, K.; Tatsuta, Y., Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions, J. High Energy Phys., 1406, 017 (2014)
[30] Kobayashi, T.; Nilles, H. P.; Ploger, F.; Raby, S.; Ratz, M., Stringy origin of non-Abelian discrete flavor symmetries, Nucl. Phys. B, 768, 135-156 (2007) · Zbl 1117.81354
[31] Kobayashi, T.; Raby, S.; Zhang, R.-J., Searching for realistic 4d string models with a Pati-Salam symmetry: orbifold grand unified theories from heterotic string compactification on a Z(6) orbifold, Nucl. Phys. B, 704, 3-55 (2005) · Zbl 1198.81158
[32] Ko, P.; Kobayashi, T.; Park, J.-h.; Raby, S., String-derived \(D(4)\) flavor symmetry and phenomenological implications, Phys. Rev. D, 76, 035005 (2007)
[33] Hamada, Y.; Kobayashi, T., Massive modes in magnetized brane models, Prog. Theor. Phys., 128, 903-923 (2012)
[34] Sakamoto, M.; Tanimura, S., An extension of Fourier analysis for the \(n\) torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian, J. Math. Phys., 44, 5042-5069 (2003) · Zbl 1062.81037
[35] Antoniadis, I.; Maillard, T., Moduli stabilization from magnetic fluxes in type I string theory, Nucl. Phys. B, 716, 3-32 (2005) · Zbl 1207.81098
[36] Antoniadis, I.; Kumar, A.; Panda, B., Fermion wavefunctions in magnetized branes: theta identities and Yukawa couplings, Nucl. Phys. B, 823, 116-173 (2009) · Zbl 1196.81188
[37] Choi, K.-S.; Kobayashi, T.; Maruyama, R.; Murata, M.; Nakai, Y., \(E(6, 7, 8)\) magnetized extra dimensional models, Eur. Phys. J. C, 67, 273-282 (2010)
[38] Kobayashi, T.; Maruyama, R.; Murata, M.; Ohki, H.; Sakai, M., Three-generation models from \(E_8\) magnetized extra dimensional theory, J. High Energy Phys., 1005, 050 (2010) · Zbl 1287.81124
[39] Di Vecchia, P.; Marotta, R.; Pesando, I.; Pezzella, F., Open strings in the system D5/D9, J. Phys. A, 44, 245401 (2011) · Zbl 1222.81234
[40] Abe, H.; Kobayashi, T.; Ohki, H.; Sumita, K., Superfield description of 10D SYM theory with magnetized extra dimensions, Nucl. Phys. B, 863, 1-18 (2012) · Zbl 1246.81347
[41] De Angelis, L.; Marotta, R.; Pezzella, F.; Troise, R., More about branes on a general magnetized torus, J. High Energy Phys., 1210, 052 (2012)
[42] Abe, H.; Kobayashi, T.; Ohki, H.; Sumita, K.; Tatsuta, Y., Flavor landscape of 10D SYM theory with magnetized extra dimensions
[43] Ferrer, E. J.; de la Incera, V., Mass eigenvalues of the open charged string in a magnetic background, Phys. Rev. D, 52, 1011-1018 (1995)
[44] Ferrer, E. J.; de la Incera, V., Global symmetries of open strings in an electromagnetic background, Phys. Rev. D, 49, 2926-2932 (1994)
[45] Di Vecchia, P.; Liccardo, A.; Marotta, R.; Pesando, I.; Pezzella, F., Wrapped magnetized branes: two alternative descriptions?, J. High Energy Phys., 0711, 100 (2007)
[46] Dixon, L. J.; Harvey, J. A.; Vafa, C.; Witten, E., Strings on orbifolds, Nucl. Phys. B, 261, 678-686 (1985)
[47] Dixon, L. J.; Harvey, J. A.; Vafa, C.; Witten, E., Strings on orbifolds. 2, Nucl. Phys. B, 274, 285-314 (1986)
[48] Kawamura, Y., Gauge symmetry breaking from extra space \(S^1 / Z_2\), Prog. Theor. Phys., 103, 613-619 (2000)
[49] Kawamura, Y., Split multiplets, coupling unification and extra dimension, Prog. Theor. Phys., 105, 691-696 (2001) · Zbl 0990.81151
[50] Kawamura, Y., Triplet doublet splitting, proton stability and extra dimension, Prog. Theor. Phys., 105, 999-1006 (2001)
[51] Katsuki, Y.; Kawamura, Y.; Kobayashi, T.; Ohtsubo, N.; Ono, Y., \(Z(N)\) orbifold models, Nucl. Phys. B, 341, 611-640 (1990) · Zbl 0970.81061
[52] Kobayashi, T.; Ohtsubo, N., Geometrical aspects of \(Z(N)\) orbifold phenomenology, Int. J. Mod. Phys. A, 9, 87-126 (1994) · Zbl 0985.81631
[53] Choi, K.-S.; Kim, J. E., Quarks and leptons from orbifolded superstring, Lect. Notes Phys., 696, 1-406 (2006) · Zbl 1114.81002
[54] Kawamura, Y.; Kinami, T.; Miura, T., Equivalence classes of boundary conditions in gauge theory on \(Z(3)\) orbifold, Prog. Theor. Phys., 120, 815-831 (2008) · Zbl 1165.81397
[55] Kawamura, Y.; Miura, T., Equivalence classes of boundary conditions in \(SU(N)\) gauge theory on 2-dimensional orbifolds, Prog. Theor. Phys., 122, 847-864 (2010) · Zbl 1181.81115
[56] Kawamura, Y.; Kinami, T.; Oda, K.-y., Orbifold family unification, Phys. Rev. D, 76, 035001 (2007)
[57] Kawamura, Y.; Miura, T., Orbifold family unification in \(SO(2 N)\) gauge theory, Phys. Rev. D, 81, 075011 (2010)
[58] Goto, Y.; Kawamura, Y.; Miura, T., Orbifold family unification on 6 dimensions, Phys. Rev. D, 88, 055016 (2013)
[59] Abe, H.; Kobayashi, T.; Ohki, H., Magnetized orbifold models, J. High Energy Phys., 0809, 043 (2008) · Zbl 1245.81254
[60] Abe, H.; Choi, K.-S.; Kobayashi, T.; Ohki, H., Three generation magnetized orbifold models, Nucl. Phys. B, 814, 265-292 (2009) · Zbl 1194.81248
[61] Groot Nibbelink, S.; Vaudrevange, P. K., Schoen manifold with line bundles as resolved magnetized orbifolds, J. High Energy Phys., 1303, 142 (2013) · Zbl 1342.81462
[62] Fujimoto, Y.; Kobayashi, T.; Miura, T.; Nishiwaki, K.; Sakamoto, M., Shifted orbifold models with magnetic flux, Phys. Rev. D, 87, 086001 (2013)
[63] Abe, T.-H.; Fujimoto, Y.; Kobayashi, T.; Miura, T.; Nishiwaki, K., \(Z_N\) twisted orbifold models with magnetic flux, J. High Energy Phys., 1401, 065 (2014)
[64] Scherk, J.; Schwarz, J. H., Spontaneous breaking of supersymmetry through dimensional reduction, Phys. Lett. B, 82, 60 (1979)
[65] Scherk, J.; Schwarz, J. H., How to get masses from extra dimensions, Nucl. Phys. B, 153, 61-88 (1979)
[66] Ibanez, L. E.; Nilles, H. P.; Quevedo, F., Orbifolds and Wilson lines, Phys. Lett. B, 187, 25-32 (1987)
[67] Kobayashi, T.; Ohtsubo, N., Analysis on the Wilson lines of \(Z(N)\) orbifold models, Phys. Lett. B, 257, 56-62 (1991)
[68] Angelantonj, C.; Cardella, M.; Irges, N., Scherk-Schwarz breaking and intersecting branes, Nucl. Phys. B, 725, 115-154 (2005) · Zbl 1178.81210
[69] Blumenhagen, R.; Cvetic, M.; Marchesano, F.; Shiu, G., Chiral D-brane models with frozen open string moduli, J. High Energy Phys., 0503, 050 (2005)
[70] Angelantonj, C.; Condeescu, C.; Dudas, E.; Lennek, M., Stringy instanton effects in models with rigid magnetised D-branes, Nucl. Phys. B, 818, 52-94 (2009) · Zbl 1194.81180
[71] Forste, S.; Honecker, G., Rigid D6-branes on \(T^6 /(Z_2 \times Z_{2 M} \times \Omega R)\) with discrete torsion, J. High Energy Phys., 1101, 091 (2011) · Zbl 1214.81209
[72] Hashimoto, A.; Taylor, W., Fluctuation spectra of tilted and intersecting D-branes from the Born-Infeld action, Nucl. Phys. B, 503, 193-219 (1997) · Zbl 0979.81572
[73] Hamada, Y.; Kobayashi, T.; Uemura, S., Flavor structure in D-brane models: Majorana neutrino mases
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.