Abstract
We consider realistic F-theory GUT models based on discrete family symmetries A 4 and S 3, combined with SU(5) GUT, comparing our results to existing field theory models based on these groups. We provide an explicit calculation to support the emergence of the family symmetry from the discrete monodromies arising in F-theory. We work within the spectral cover picture where in the present context the discrete symmetries are associated to monodromies among the roots of a five degree polynomial and hence constitute a subgroup of the S 5 permutation symmetry. We focus on the cases of A 4 and S 3 subgroups, motivated by successful phenomenological models interpreting the fermion mass hierarchy and in particular the neutrino data. More precisely, we study the implications on the effective field theories by analysing the relevant discriminants and the topological properties of the polynomial coefficients, while we propose a discrete version of the doublet-triplet splitting mechanism.
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References
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
R. Donagi and M. Wijnholt, Model building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory — II: experimental predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [INSPIRE].
R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, Global F-theory GUTs, Nucl. Phys. B 829 (2010) 325 [arXiv:0908.1784] [INSPIRE].
J.J. Heckman and C. Vafa, Flavor hierarchy from F-theory, Nucl. Phys. B 837 (2010) 137 [arXiv:0811.2417] [INSPIRE].
J.J. Heckman, J. Marsano, N. Saulina, S. Schäfer-Nameki and C. Vafa, Instantons and SUSY breaking in F-theory, arXiv:0808.1286 [INSPIRE].
R. Blumenhagen, V. Braun, T.W. Grimm and T. Weigand, GUTs in type IIB orientifold compactifications, Nucl. Phys. B 815 (2009) 1 [arXiv:0811.2936] [INSPIRE].
F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [INSPIRE].
T. Weigand, Lectures on F-theory compactifications and model building, Class. Quant. Grav. 27 (2010) 214004 [arXiv:1009.3497] [INSPIRE].
J.J. Heckman, Particle physics implications of F-theory, Ann. Rev. Nucl. Part. Sci. 60 (2010) 237 [arXiv:1001.0577] [INSPIRE].
T.W. Grimm, The N = 1 effective action of F-theory compactifications, Nucl. Phys. B 845 (2011) 48 [arXiv:1008.4133] [INSPIRE].
G.K. Leontaris, Aspects of F-theory GUTs, PoS(CORFU2011)095 [arXiv:1203.6277] [INSPIRE].
A. Maharana and E. Palti, Models of particle physics from type IIB string theory and F-theory: a review, Int. J. Mod. Phys. A 28 (2013) 1330005 [arXiv:1212.0555] [INSPIRE].
J.J. Heckman, A. Tavanfar and C. Vafa, The point of E 8 in F-theory GUTs, JHEP 08 (2010) 040 [arXiv:0906.0581] [INSPIRE].
R. Donagi and M. Wijnholt, Breaking GUT groups in F-theory, Adv. Theor. Math. Phys. 15 (2011) 1523 [arXiv:0808.2223] [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, Monodromies, fluxes and compact three-generation F-theory GUTs, JHEP 08 (2009) 046 [arXiv:0906.4672] [INSPIRE].
H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, Flavor structure in F-theory compactifications, JHEP 08 (2010) 036 [arXiv:0910.2762] [INSPIRE].
E. Dudas and E. Palti, On hypercharge flux and exotics in F-theory GUTs, JHEP 09 (2010) 013 [arXiv:1007.1297] [INSPIRE].
S.F. King, G.K. Leontaris and G.G. Ross, Family symmetries in F-theory GUTs, Nucl. Phys. B 838 (2010) 119 [arXiv:1005.1025] [INSPIRE].
J.C. Callaghan, S.F. King, G.K. Leontaris and G.G. Ross, Towards a realistic F-theory GUT, JHEP 04 (2012) 094 [arXiv:1109.1399] [INSPIRE].
I. Antoniadis and G.K. Leontaris, Building SO(10) models from F-theory, JHEP 08 (2012) 001 [arXiv:1205.6930] [INSPIRE].
J.C. Callaghan and S.F. King, E 6 models from F-theory, JHEP 04 (2013) 034 [arXiv:1210.6913] [INSPIRE].
R. Tatar and W. Walters, GUT theories from Calabi-Yau 4-folds with SO(10) singularities, JHEP 12 (2012) 092 [arXiv:1206.5090] [INSPIRE].
J.C. Callaghan, S.F. King and G.K. Leontaris, Gauge coupling unification in E 6 F-theory GUTs with matter and bulk exotics from flux breaking, JHEP 12 (2013) 037 [arXiv:1307.4593] [INSPIRE].
L.E. Ibáñez and G.G. Ross, Discrete gauge symmetry anomalies, Phys. Lett. B 260 (1991) 291 [INSPIRE].
P. Anastasopoulos, M. Cvetič, R. Richter and P.K.S. Vaudrevange, String constraints on discrete symmetries in MSSM type II quivers, JHEP 03 (2013) 011 [arXiv:1211.1017] [INSPIRE].
H.M. Lee et al., A unique Z R4 symmetry for the MSSM, Phys. Lett. B 694 (2011) 491 [arXiv:1009.0905] [INSPIRE].
L.E. Ibáñez, A.N. Schellekens and A.M. Uranga, Discrete gauge symmetries in discrete MSSM-like orientifolds, Nucl. Phys. B 865 (2012) 509 [arXiv:1205.5364] [INSPIRE].
G. Honecker and W. Staessens, To tilt or not to tilt: discrete gauge symmetries in global intersecting D-brane models, JHEP 10 (2013) 146 [arXiv:1303.4415] [INSPIRE].
M. Berasaluce-Gonzalez, P.G. Camara, F. Marchesano, D. Regalado and A.M. Uranga, Non-abelian discrete gauge symmetries in 4D string models, JHEP 09 (2012) 059 [arXiv:1206.2383] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
S.F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, Neutrino mass and mixing: from theory to experiment, New J. Phys. 16 (2014) 045018 [arXiv:1402.4271] [INSPIRE].
I. Antoniadis and G.K. Leontaris, Neutrino mass textures from F-theory, Eur. Phys. J. C 73 (2013) 2670 [arXiv:1308.1581] [INSPIRE].
R. Donagi and M. Wijnholt, Higgs bundles and UV completion in F-theory, Commun. Math. Phys. 326 (2014) 287 [arXiv:0904.1218] [INSPIRE].
S. Cecotti, M.C.N. Cheng, J.J. Heckman and C. Vafa, Yukawa couplings in F-theory and non-commutative geometry, arXiv:0910.0477 [INSPIRE].
L. Aparicio, A. Font, L.E. Ibáñez and F. Marchesano, Flux and instanton effects in local F-theory models and hierarchical fermion masses, JHEP 08 (2011) 152 [arXiv:1104.2609] [INSPIRE].
F. Marchesano and L. Martucci, Non-perturbative effects on seven-brane Yukawa couplings, Phys. Rev. Lett. 104 (2010) 231601 [arXiv:0910.5496] [INSPIRE].
A. Font, F. Marchesano, D. Regalado and G. Zoccarato, Up-type quark masses in SU(5) F-theory models, JHEP 11 (2013) 125 [arXiv:1307.8089] [INSPIRE].
C. Mayrhofer, E. Palti and T. Weigand, Hypercharge flux in IIB and F-theory: anomalies and gauge coupling unification, JHEP 09 (2013) 082 [arXiv:1303.3589] [INSPIRE].
S.F. King, Neutrino mass models, Rept. Prog. Phys. 67 (2004) 107 [hep-ph/0310204] [INSPIRE].
N. Nakayama, On Weierstrass models, Algebraic Geometry and Commutative Algebra, Kinokuniya, Tokyo Japan (1988).
V. Bouchard, J.J. Heckman, J. Seo and C. Vafa, F-theory and neutrinos: Kaluza-Klein dilution of flavor hierarchy, JHEP 01 (2010) 061 [arXiv:0904.1419] [INSPIRE].
M.C. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, Global fit to three neutrino mixing: critical look at present precision, JHEP 12 (2012) 123 [arXiv:1209.3023] [INSPIRE].
J. Lesgourgues and S. Pastor, Neutrino mass from cosmology, Adv. High Energy Phys. 2012 (2012) 608515 [arXiv:1212.6154] [INSPIRE].
D.C. Latimer and D.J. Ernst, Physical region for three-neutrino mixing angles, Phys. Rev. D 71 (2005) 017301 [nucl-th/0405073] [INSPIRE].
P. Huber, On the determination of anti-neutrino spectra from nuclear reactors, Phys. Rev. C 84 (2011) 024617 [Erratum ibid. C 85 (2012) 029901] [arXiv:1106.0687] [INSPIRE].
G.K. Leontaris and G.G. Ross, Yukawa couplings and fermion mass structure in F-theory GUTs, JHEP 02 (2011) 108 [arXiv:1009.6000] [INSPIRE].
C. Mayrhofer, E. Palti and T. Weigand, U(1) symmetries in F-theory GUTs with multiple sections, JHEP 03 (2013) 098 [arXiv:1211.6742] [INSPIRE].
J. Borchmann, C. Mayrhofer, E. Palti and T. Weigand, Elliptic fibrations for SU(5) × U(1) × U(1) F-theory vacua, Phys. Rev. D 88 (2013) 046005 [arXiv:1303.5054] [INSPIRE].
V. Braun, T.W. Grimm and J. Keitel, Geometric engineering in toric F-theory and GUTs with U(1) gauge factors, JHEP 12 (2013) 069 [arXiv:1306.0577] [INSPIRE].
M. Cvetič, D. Klevers and H. Piragua, F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections, JHEP 06 (2013) 067 [arXiv:1303.6970] [INSPIRE].
M. Cvetič, D. Klevers, H. Piragua and P. Song, Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1) × U(1) × U(1) gauge symmetry, JHEP 03 (2014) 021 [arXiv:1310.0463] [INSPIRE].
J. Marsano, Hypercharge flux, exotics and anomaly cancellation in F-theory GUTs, Phys. Rev. Lett. 106 (2011) 081601 [arXiv:1011.2212] [INSPIRE].
S. Krippendorf, D.K. Mayorga Pena, P.-K. Oehlmann and F. Ruehle, Rational F-theory GUTs without exotics, JHEP 07 (2014) 013 [arXiv:1401.5084] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. (2014) [arXiv:1303.5076] [INSPIRE].
A. Font, L.E. Ibáñez, F. Marchesano and D. Regalado, Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) Unification, JHEP 03 (2013) 140 [Erratum ibid. 1307 (2013) 036] [arXiv:1211.6529] [INSPIRE].
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Karozas, A., King, S.F., Leontaris, G.K. et al. Discrete family symmetry from F-theory GUTs. J. High Energ. Phys. 2014, 107 (2014). https://doi.org/10.1007/JHEP09(2014)107
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DOI: https://doi.org/10.1007/JHEP09(2014)107