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Wavefunctions on \(S^2\) with flux and branes. (English) Zbl 1418.83053
Summary: We formulate a six dimensional U(1) gauge theory compactified on a (two dimensional) sphere \(S^2\) with flux and localized brane sources. Profiles of the lowest Kaluza-Klein (KK) wavefunctions and their masses are derived analytically. In contrast to ordinary sphere compactifications, the above setup can lead to the degeneracy of and the sharp localizations of the linearly independent lowest KK modes, depending on the number of branes and their tensions. Moreover, it can naturally accommodate CP violation in Yukawa interactions.
MSC:
83E15 Kaluza-Klein and other higher-dimensional theories
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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References:
[1] Atiyah, MF; Singer, IM, The index of elliptic operators on compact manifolds, Bull. Am. Math. Soc., 69, 422, (1969) · Zbl 0118.31203
[2] Cremades, D.; Ibáñez, LE; Marchesano, F., Computing Yukawa couplings from magnetized extra dimensions, JHEP, 05, 079, (2004)
[3] Conlon, JP; Maharana, A.; Quevedo, F., Wave functions and Yukawa couplings in local string compactifications, JHEP, 09, 104, (2008) · Zbl 1245.83057
[4] Abe, H.; Choi, K-S; Kobayashi, T.; Ohki, H., Three generation magnetized orbifold models, Nucl. Phys., B 814, 265, (2009) · Zbl 1194.81248
[5] Abe, H.; etal., Phenomenological aspects of 10D SYM theory with magnetized extra dimensions, Nucl. Phys., B 870, 30, (2013) · Zbl 1262.81250
[6] Abe, H.; etal., Flavor landscape of 10D SYM theory with magnetized extra dimensions, JHEP, 04, 007, (2014)
[7] Abe, T-h; etal., Classification of three-generation models on magnetized orbifolds, Nucl. Phys., B 894, 374, (2015) · Zbl 1328.81219
[8] Buchmüller, W.; Dierigl, M.; Ruehle, F.; Schweizer, J., Split symmetries, Phys. Lett., B 750, 615, (2015) · Zbl 1364.83058
[9] N. Arkani-Hamed and M. Schmaltz, Hierarchies without symmetries from extra dimensions, Phys. Rev.D 61 (2000) 033005 [hep-ph/9903417] [INSPIRE].
[10] D.E. Kaplan and T.M.P. Tait, Supersymmetry breaking, fermion masses and a small extra dimension, JHEP06 (2000) 020 [hep-ph/0004200] [INSPIRE]. · Zbl 0990.81777
[11] S.J. Huber and Q. Shafi, Fermion masses, mixings and proton decay in a Randall-Sundrum model, Phys. Lett.B 498 (2001) 256 [hep-ph/0010195] [INSPIRE].
[12] Abe, H.; Kobayashi, T.; Sumita, K.; Tatsuta, Y., Gaussian Froggatt-Nielsen mechanism on magnetized orbifolds, Phys. Rev., D 90, 105006, (2014)
[13] Fujimoto, Y.; etal., Comprehensive analysis of Yukawa hierarchies on T2/Z_{N} with magnetic fluxes, Phys. Rev., D 94, (2016)
[14] Kobayashi, T.; Nishiwaki, K.; Tatsuta, Y., CP-violating phase on magnetized toroidal orbifolds, JHEP, 04, 080, (2017)
[15] Abe, H.; Choi, K-S; Kobayashi, T.; Ohki, H., Non-abelian discrete flavor symmetries from magnetized/intersecting brane models, Nucl. Phys., B 820, 317, (2009) · Zbl 1194.81178
[16] Abe, H.; etal., Non-abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions, JHEP, 06, 017, (2014)
[17] Higaki, T.; Tatsuta, Y., Inflation from periodic extra dimensions, JCAP, 07, 011, (2017)
[18] Randjbar-Daemi, S.; Salvio, A.; Shaposhnikov, M., On the decoupling of heavy modes in Kaluza-Klein theories, Nucl. Phys., B 741, 236, (2006) · Zbl 1214.83030
[19] Wu, TT; Yang, CN, Dirac monopole without strings: monopole harmonics, Nucl. Phys., B 107, 365, (1976)
[20] Wu, TT; Yang, CN, Dirac’s monopole without strings: classical Lagrangian theory, Phys. Rev., D 14, 437, (1976)
[21] M. Troyanov, F.J. Carreras, O. Gil-Medrano and A. Naveira, Metrics of constant curvature on a sphere with two conical singularities, in Differntial Geometry, F.J. Carreras et al. eds., Springer, Germany (1989).
[22] Umehara, M.; Yamada, K., Metrics of constant curvature 1 with three conical singularities on 2-sphere, Illinois J. Math., 44, 72, (1998) · Zbl 0958.30029
[23] Redi, M., Footballs, conical singularities and the Liouville equation, Phys. Rev., D 71, (2005)
[24] A. Eremenko, Metrics of positive curvature with conic singularities on the sphere, Proc. Amer. Math. Soc.132 (2004) 3349 [math/0208025].
[25] Salam, A.; Sezgin, E., Chiral compactification on Minkowski ×S2 of N = 2 Einstein-Maxwell supergravity in six-dimensions, Phys. Lett., B 147, 47, (1984)
[26] Aghababaie, Y.; Burgess, CP; Parameswaran, SL; Quevedo, F., Towards a naturally small cosmological constant from branes in 6D supergravity, Nucl. Phys., B 680, 389, (2004) · Zbl 1036.83025
[27] Gibbons, GW; Güven, R.; Pope, CN, 3-branes and uniqueness of the Salam-Sezgin vacuum, Phys. Lett., B 595, 498, (2004) · Zbl 1247.81373
[28] Parameswaran, SL; Randjbar-Daemi, S.; Salvio, A., Gauge fields, fermions and mass gaps in 6D brane worlds, Nucl. Phys., B 767, 54, (2007) · Zbl 1117.83381
[29] Troyanov, M., Prescribing curvature on compact surfaces with conical singularities, Trans. Amer. Math. Soc., 324, 793, (1991) · Zbl 0724.53023
[30] Lee, HM; Lüdeling, C., The general warped solution with conical branes in six-dimensional supergravity, JHEP, 01, 062, (2006)
[31] C. Ludeling, 6D supergravity: warped solution and gravity mediated supersymmetry breaking, Ph.D. thesis, Hamburg University, Hamburg, Germany (2006).
[32] Mondello, G.; Panov, D., Spherical metrics with conical singularities on a 2-sphere: angle constraints, Int. Math. Res. Not., 2016, 4937, (2015) · Zbl 1446.53027
[33] Buchmüller, W.; Schweizer, J., Flavor mixings in flux compactifications, Phys. Rev., D 95, (2017)
[34] Buchmüller, W.; Patel, KM, Flavor physics without flavor symmetries, Phys. Rev., D 97, (2018)
[35] Ishida, M.; Nishiwaki, K.; Tatsuta, Y., Brane-localized masses in magnetic compactifications, Phys. Rev., D 95, (2017)
[36] Ishida, M.; Nishiwaki, K.; Tatsuta, Y., Seesaw mechanism in magnetic compactifications, JHEP, 07, 125, (2018)
[37] H. Abe, M. Ishida and Y. Tatsuta, Effects of localized μ-terms at the fixed points in magnetized orbifold models, arXiv:1806.10369 [INSPIRE].
[38] Buchmüller, W.; Dierigl, M.; Ruehle, F.; Schweizer, J., Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux, Phys. Rev., D 92, 105031, (2015)
[39] Buchmüller, W.; Dierigl, M.; Tatsuta, Y., Magnetized orbifolds and localized flux, Annals Phys., 401, 91, (2019) · Zbl 1415.81041
[40] C.S. Lim, The implication of gauge-Higgs unification for the hierarchical fermion masses, PTEP2018 (2018) 093B02 [arXiv:1801.01639] [INSPIRE].
[41] Hosotani, Y., Dynamical mass generation by compact extra dimensions, Phys. Lett., B 126, 309, (1983)
[42] Hatanaka, H.; Inami, T.; Lim, CS, The gauge hierarchy problem and higher dimensional gauge theories, Mod. Phys. Lett., A 13, 2601, (1998)
[43] Buchmüller, W.; Dierigl, M.; Dudas, E.; Schweizer, J., Effective field theory for magnetic compactifications, JHEP, 04, 052, (2017) · Zbl 1378.83081
[44] Ghilencea, DM; Lee, HM, Wilson lines and UV sensitivity in magnetic compactifications, JHEP, 06, 039, (2017) · Zbl 1380.81400
[45] Buchmüller, W.; Dierigl, M.; Dudas, E., Flux compactifications and naturalness, JHEP, 08, 151, (2018) · Zbl 1396.81127
[46] Chou, KS; Wan, TYH, Asymptotic radial symmetry for solutions of Δu + eu = 0 in a punctured disc, Pacific J. Math., 163, 269, (1994) · Zbl 0794.35049
[47] Brion, M., Homogeneous projective bundles over abelian varieties, Alg. Numb. Theor., 7, 2475, (2013) · Zbl 1315.14057
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