Abstract
We begin with an E8 x E8 Heterotic model broken to an SU(5)gauge and a mirror SU(5)gauge, where one SU(5) and its spectrum is identified as the visible sector while the other can be identified as a hidden mirror world. In both cases we obtain the minimal supersymmetric standard model spectrum after Wilson-line symmetry-breaking enhanced by a low energy R-parity enforced by a local (or global) U(1)x-symmetry. Using Heterotic/F-theory duality, we show how to eliminate the vector-like exotics which were obtained in previous constructions. In these constructions, the Calabi-Yau [CY] four-fold was defined by an elliptic fibration with section over a base B3 and a GUT surface given by K3/ℤ2 = Enriques surface. In the present paper we construct a quotient CY four-fold fibered by tori with two elliptic structures given by a pair of sections fibered over the Enriques surface. Using Heterotic/F-theory duality we are able to define the cohomologies used to derive the massless spectrum. Our model for the 'correct' F-theory dual of a Heterotic model with Wilson-line symmetry-breaking builds on prior literature but employs the stack-theoretic version of the dictionary between the Heterotic semi-stable Es-bundles with Yang-Mills connection and the dP9-fibrations used to construct the F-theory dual.
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References
A. Anandakrishnan and S. Raby, SU(6) GUT Breaking on a Projective Plane, Nucl. Phys.B 868 (2013) 627 [arXiv:1205.1228] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and E. Palti, Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds, Phys. Rev.A 84 (2011) 106005 [arXiv:1106.4804] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and E. Palti, Heterotic Line Bundle Standard Models, JHEP06 (2012) 113 [arXiv:1202.1757] [INSPIRE].
R. Barbieri, T. Gregoire and L.J. Hall, Mirror world at the large hadron collider, hep-ph/0509242 [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory -I, JHEP01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Brane s in F-theory -II: Experimental Predictions, JHEP01 (2009) 059 [arXiv:0806.0102] [INSPIRE].
Z.G. Berezhiani, Astrophysical implications of the mirror world with broken mirror parity, Acta Phys. Polan.B 27 (1996) 1503 [hep-ph/9602326] [INSPIRE].
R. Blumenhagen, V. Braun, T.W. Grimm and T. Weigand, GUTs in Type JIB Orientifold Compactifications, Nucl. Phys.B 815 (2009) 1 [arXiv:0811.2936] [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].
R. Blumenhagen, Gauge Coupling Unification in F-theory Grand Unified Theories, Phys. Rev. Lett.102 (2009) 071601 [arXiv:0812.0248] [INSPIRE].
E. Brieskorn, Singular elements of semi-simple algebraic groups, in proceedings of the Congrès International des Mathématiciens, Nice, France, 1-10 Septembre 1970, in Actes du Congrès International des Mathématiciens. Tome 2, Gauthier-Villars, Paris France (1971), pp. 279-284.
F. Catanese, Automorphisms of rational double points and moduli space s of surface s of general type, Compos. Math.61 (1987) 81.
Z. Chacko, H.-S. Goh and R. Harnik, The Twin Higgs: Natural electroweak breaking from mirror symmetry, Phys. Rev. Lett.96 (2006) 231802 [hep-ph/0506256] [INSPIRE].
H. Clemens and S. Raby, Heterotic/ F-theory Duality and Narasimhan-Seshadri Equivalence, arXiv:1906.07238 [INSPIRE].
H. Clemens and S. Raby, F-theory over a Fano threefold built from A 4-roots, arXiv: 1908.01110 [INSPIRE].
R. Davies, Dirac gauginos and unification in F-theory, JHEP10 (2012) 010 [arXiv:1205.1942v3] [INSPIRE].
S. Dimopoulos, S. Raby and F. Wilczek, Supersymmetry and the Scale of Unification, Phys. Rev.D 24 (1981) 1681 [INSPIRE].
S. Dimopoulos and H. Georgi, Softly Broken Supersymmetry and SU(5), Nucl. Phys.B 193 (1981) 150 [INSPIRE].
M.J. Dolan, J. Marsano and S. Schüfer-Nameki, Unification and Phenomenology of F-theory GUTs with U(1)PQ, JHEP12 (2011) 032 [arXiv:1109.4958] [INSPIRE].
R. Donagi and M. Wijnholt, Model Building with F-theory, Adv. Theor. Math. Phys.15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].
R. Donagi and M. Wijnholt, Breaking GUT Groups in F-theory, Adv. Theor. Math. Phys.15 (2011) 1523 [arXiv:0808.2223v2] [INSPIRE].
R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, The Spectra of heterotic standard model vacua, JHEP06 (2005) 070 [hep-th/0411156] [INSPIRE].
R. Friedman, J. Morgan and E. Witten, Vector bundles and F-theory, Commun. Math. Phys.187 (1997) 679 [hep-th/9701162] [INSPIRE].
T.W. Grimm and T. Weigand, On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs, Phys. Rev.D 82 (2010) 086009 [arXiv:1006.0226] [INSPIRE].
T.W. Grimm, M. Kerstan, E. Palti and T. Weigand, Massive Abelia n Gauge Symmetries and Fluxes in F-theory, JHEP12 (2011) 004 [arXiv:1107.3842] [INSPIRE].
H. Hayashi, R. Tatar, Y. Toda, T. Watari and M. Yamazaki, New Aspects of Heterotic-F Theory Duality, Nucl. Phys.B 806 (2009) 224 [arXiv:0805.1057] [INSPIRE].
A. Hebecker and M. Trapletti, Gauge unification in highly anisotropic string compactifications, Nucl. Phys.B 713 (2005) 173 [hep-th/0411131] [INSPIRE].
A. Hebecker and J. Unwin, Precision Unification and Proton Decay in F-theory G UTs with High Scale Super symmetry, JHEP09 (2014) 125 [arXiv:1405.2930] [INSPIRE].
L.E. Ibáñez and G.G. Ross, Low-Energy Predictions in Supersymmetric Grand Unified Theories, Phys. Lett.B 105 (1981) 439 [INSPIRE].
V. Kac, Infinite-dimensional Lie algebras, Cambridge University Press, Cambridge U.K. (1990).
Y. Kawamata andY. Namikawa, Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi- Yau varieties, Invent. Math.118 (1994) 395.
J.E. Kim, J.-H. Kim and B. Kyae, Superstring standard model from ℤ12- Iorbifold compactification with and without exotics and effective R-parity, JHEP06 (2007) 034 [hep-ph/0702278] [INSPIRE].
S. Krippendorf, H.P. Nilles, M. Ratz and M.W. Winkler, Hidden SUSY from precision gauge unification, Phys. Rev.D 88 (2013) 035022 [arXiv:1306.0574] [INSPIRE].
M. Kuntzler and S. Schiifer-Nameki, Tate Trees for Elliptic Fibrations with Rank one Mordell-Weil group, arXiv:1406.5174 [INSPIRE].
C. Lawrie, S. Schiifer-Nameki and J.-M. Wong, F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections, JHEP09 (2015) 144 [arXiv:1504.05593] [INSPIRE].
O. Lebedev et al., A Mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett. B 645 (2007) 88 [hep-th/0611095] [INSPIRE].
O. Lebedev, H.P. Nilles, S. Ramos-Sanchez, M. Ratz and P.K.S. Vaudrevange, Heterotic mini-landscape ( II): Completing the search for MSSM vacua in a ℤ6orbifold, Phys. Lett. B 668 (2008) 331 [arXiv: 0807.4384] [INSPIRE].
O. Lebedev et al., The Heterotic Road to the MSSM with R parity, Phys. Rev. D 77 (2008) 046013 [arXiv:0708.2691] [INSPIRE].
H.M. Lee et al., A unique ℤ4R-symmetry for the MSSM, Phy. Lett.B 694 (2011) 491 [arXiv:1009.0905] [INSPIRE].
H.M. Lee et al., Discrete R symmetries for the MSSM and its singlet extensions, Nucl. Phys.B 850 (2011) 1 [arXiv:1102.3595] [INSPIRE].
E. Looijenga, Root Systems And Elliptic Curves, Invent. Math. 38 (1977) 17.
J. Marsano and S. Schiifer-Nameki, Yukawas, G-fiux and Spectral Covers from Resolved Calabi- Yau's, JHEP 11 (2011) 098 [arXiv:1108.1794] [INSPIRE].
J. Marsano, H. Clemens, T. Pantev, S. Raby and H.-H. Tseng, A Global SU(5) F-theory model with Wilson line breaking, JHEP 01 (2013) 150 [arXiv:1206.6132] [INSPIRE].
C. Mayrhofer, E. Palti and T. Weigand, Hypercharge Flux in JIB and F-theory: Anomalies and Gauge Coupling Unification, JHEP 09 (2013) 082 [arXiv:1303.3589] [INSPIRE].
D.R. Morrison and D.S. Park, F- Theory and the Mordell- Weil Group of Elliptically-Fibered Calabi-Yau Threefolds, JHEP 10 (2012) 128 [arXiv:1208.2695] [INSPIRE].
D. Mumford, Theta characteristics of an algebraic curve, Ann. Sci. Éc. Norm. Super. 4 (1971) 181.
D. Mumford, Prym Varieties I, in Contributions to Analysis: A collection of papers dedicated to Lipman Bers, Academic Press (1974), pp. 325-350.
L.B. Okun, Mirror particles and mirror matter: 50 years of speculations and search, Phys. Usp.50 (2007) 380 [hep-ph/0606202] [INSPIRE].
S. Raby, M. Ratz and K. Schmidt-Hoberg, Precision gauge unification in the MSSM, Phys. Lett.B 687 (2010) 342 [arXiv:0911.4249] [INSPIRE].
G.G. Ross, Wilson line breaking and gauge coupling unification, hep-ph/0411057 [INSPIRE].
P. Slodowy, Simple singularities and simple algebraic groups, Springer-Verlag, Lect . Notes Math.815 (1980) 1.
R. Tatar, Y. Tsuchiya and T. Watari, Right-handed Neutrinos in F-theory Compactifications, Nucl. Phys.B 823 (2009) 1 [arXiv:0905.2289] [INSPIRE].
M. Trapletti, Gauge symmetry breaking in orbifold model building, Mod. Phys. Lett.A 21 (2006) 2251 [hep-th/0611030] [INSPIRE].
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ArXiv ePrint: 1908.01913
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Clemens, H., Raby, S. Heterotic-F-theory duality with Wilson line symmetry-breaking. J. High Energ. Phys. 2019, 16 (2019). https://doi.org/10.1007/JHEP12(2019)016
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DOI: https://doi.org/10.1007/JHEP12(2019)016