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Schoen manifold with line bundles as resolved magnetized orbifolds. (English) Zbl 1342.81462
Summary: We give an alternative description of the Schoen manifold as the blow-up of a \(2\times 2\) orbifold in which one 2-factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained in heterotic string compactifications using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an \(E_8\times E_8'\) heterotic \(\mathrm{SU}(5)\) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard heterotic orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by G. Aldazabal et al. [Nucl. Phys., B 519, No. 1–2, 239–281 (1998; Zbl 0945.81050)] we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
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[1] Faraggi, AE, A new standard-like model in the four-dimensional free fermionic string formulation, Phys. Lett., B 278, 131, (1992)
[2] Cleaver, G.; Faraggi, A.; Nanopoulos, DV, String derived MSSM and M-theory unification, Phys. Lett., B 455, 135, (1999) · Zbl 1016.81506
[3] Dijkstra, T.; Huiszoon, L.; Schellekens, A., Supersymmetric standard model spectra from RCFT orientifolds, Nucl. Phys., B 710, 3, (2005) · Zbl 1115.81378
[4] Dijkstra, T.; Huiszoon, L.; Schellekens, A., Chiral supersymmetric standard model spectra from orientifolds of Gepner models, Phys. Lett., B 609, 408, (2005) · Zbl 1247.81364
[5] Dixon, LJ; Harvey, JA; Vafa, C.; Witten, E., Strings on orbifolds, Nucl. Phys., B 261, 678, (1985)
[6] Dixon, LJ; Harvey, JA; Vafa, C.; Witten, E., Strings on orbifolds. 2, Nucl. Phys., B 274, 285, (1986)
[7] Nilles, HP; Ramos-Sanchez, S.; Vaudrevange, PK; Wingerter, A., The orbifolder: a tool to study the low energy effective theory of heterotic orbifolds, Comput. Phys. Commun., 183, 1363, (2012)
[8] Lebedev, O.; etal., A mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett., B 645, 88, (2007) · Zbl 1256.81094
[9] Lebedev, O.; Nilles, HP; Ramos-Sanchez, S.; Ratz, M.; Vaudrevange, PK, Heterotic mini-landscape. (II) completing the search for MSSM vacua in a Z(6) orbifold, Phys. Lett., B 668, 331, (2008)
[10] Nibbelink Groot, S.; Held, J.; Ruehle, F.; Trapletti, M.; Vaudrevange, PK, Heterotic Z(6 − II) MSSM orbifolds in blowup, JHEP, 03, 005, (2009)
[11] Buchmüller, W.; Louis, J.; Schmidt, J.; Valandro, R., Voisin-borcea manifolds and heterotic orbifold models, JHEP, 10, 114, (2012)
[12] Blaszczyk, M.; etal., A \(Z\)_{2} × \(Z\)_{2} standard model, Phys. Lett., B 683, 340, (2010)
[13] Blaszczyk, M.; Nibbelink Groot, S.; Ruehle, F.; Trapletti, M.; Vaudrevange, PK, Heterotic MSSM on a resolved orbifold, JHEP, 09, 065, (2010) · Zbl 1291.81296
[14] Bouchard, V.; Donagi, R., An SU(5) heterotic standard model, Phys. Lett., B 633, 783, (2006) · Zbl 1247.81348
[15] Schoen, C., On fiber products of rational elliptic surfaces with section, Math. Z., 197, 177, (1988) · Zbl 0631.14032
[16] Donagi, R.; Ovrut, BA; Pantev, T.; Waldram, D., Standard model bundles on nonsimply connected Calabi-Yau threefolds, JHEP, 08, 053, (2001)
[17] Donagi, R.; Ovrut, BA; Pantev, T.; Waldram, D., Spectral involutions on rational elliptic surfaces, Adv. Theor. Math. Phys., 5, 499, (2002)
[18] Donagi, R.; He, Y-H; Ovrut, BA; Reinbacher, R., The spectra of heterotic standard model vacua, JHEP, 06, 070, (2005)
[19] Gomez, TL; Lukic, S.; Sols, I., Constraining the Kähler moduli in the heterotic standard model, Commun. Math. Phys., 276, 1, (2007) · Zbl 1134.81041
[20] Braun, V.; He, Y-H; Ovrut, BA; Pantev, T., A standard model from the \(E\)_{8} × \(E\)_{8} heterotic superstring, JHEP, 06, 039, (2005)
[21] Anderson, LB; Gray, J.; Lukas, A.; Palti, E., Two hundred heterotic standard models on smooth Calabi-Yau threefolds, Phys. Rev., D 84, 106005, (2011)
[22] Anderson, LB; Gray, J.; Lukas, A.; Palti, E., Heterotic line bundle standard models, JHEP, 06, 113, (2012)
[23] Donalson, S., Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc., 50, 1, (1985) · Zbl 0529.53018
[24] Uhlenbeck, K.; Yau, S., On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure Appl. Math., 19, 257, (1986) · Zbl 0615.58045
[25] Blumenhagen, R.; Honecker, G.; Weigand, T., Supersymmetric (non-)abelian bundles in the type I and SO(32) heterotic string, JHEP, 08, 009, (2005)
[26] Blumenhagen, R.; Honecker, G.; Weigand, T., Loop-corrected compactifications of the heterotic string with line bundles, JHEP, 06, 020, (2005)
[27] Honecker, G.; Trapletti, M., Merging heterotic orbifolds and K3 compactifications with line bundles, JHEP, 01, 051, (2007)
[28] G. Honecker, Orbifolds versus smooth heterotic compactifications, arXiv:0709.2037 [INSPIRE].
[29] Donagi, R.; Wendland, K., On orbifolds and free fermion constructions, J. Geom. Phys., 59, 942, (2009) · Zbl 1166.81033
[30] Hebecker, A.; Trapletti, M., Gauge unification in highly anisotropic string compactifications, Nucl. Phys., B 713, 173, (2005) · Zbl 1176.81102
[31] Blumenhagen, R.; Plauschinn, E., Intersecting D-branes on shift \(Z\)_{2} × \(Z\)_{2} orientifolds, JHEP, 08, 031, (2006)
[32] Fischer, M.; Ratz, M.; Torrado, J.; Vaudrevange, PK, Classification of symmetric toroidal orbifolds, JHEP, 01, 084, (2013) · Zbl 1342.81360
[33] S.J. Konopka, Non abelian orbifold compactifications of the heterotic string, arXiv:1210.5040 [INSPIRE]. · Zbl 1342.81445
[34] Cremades, D.; Ibáñez, L.; Marchesano, F., Computing Yukawa couplings from magnetized extra dimensions, JHEP, 05, 079, (2004)
[35] 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
[36] Abe, H.; Choi, K-S; Kobayashi, T.; Ohki, H., Magnetic flux, Wilson line and orbifold, Phys. Rev., D 80, 126006, (2009)
[37] Bouchard, V.; Donagi, R., On a class of non-simply connected Calabi-Yau threefolds, Commun. Num. Theor. Phys., 2, 1, (2008) · Zbl 1165.14032
[38] Denef, F.; Douglas, MR; Florea, B., Building a better racetrack, JHEP, 06, 034, (2004)
[39] Lüst, D.; Reffert, S.; Scheidegger, E.; Stieberger, S., Resolved toroidal orbifolds and their orientifolds, Adv. Theor. Math. Phys., 12, 67, (2008) · Zbl 1152.81883
[40] Groot Nibbelink, S.; Trapletti, M.; Walter, M., Resolutions of \(C\)\^{}{\(n\)}/\(Z\)_{\(n\)} orbifolds, their U(1) bundles and applications to string model building, JHEP, 03, 035, (2007)
[41] Nibbelink Groot, S.; Ha, T-W; Trapletti, M., Toric resolutions of heterotic orbifolds, Phys. Rev., D 77, 026002, (2008)
[42] Nibbelink Groot, S.; Klevers, D.; Ploger, F.; Trapletti, M.; Vaudrevange, PK, Compact heterotic orbifolds in blow-up, JHEP, 04, 060, (2008) · Zbl 1246.81251
[43] Nibbelink Groot, S., Heterotic orbifold resolutions as (2, 0) gauged linear σ-models, Fortsch. Phys., 59, 454, (2011) · Zbl 1215.81060
[44] Aldazabal, G.; Font, A.; Ibáñez, LE; Uranga, A.; Violero, G., Nonperturbative heterotic \(D\) = 6, \(D\) = 4, \(N\) = 1 orbifold vacua, Nucl. Phys., B 519, 239, (1998) · Zbl 0945.81050
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