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Hodge numbers for all CICY quotients. (English) Zbl 1373.14038
Summary: We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification [V. Braun, J. High Energy Phys. 2011, No. 4, Paper No. 005, 32 p. (2011; Zbl 1250.14026)].

MSC:
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
83E30 String and superstring theories in gravitational theory
58A14 Hodge theory in global analysis
53Z05 Applications of differential geometry to physics
Software:
CICY Quotients
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[1] Braun, V., On free quotients of complete intersection Calabi-Yau manifolds, JHEP, 04, 005, (2011) · Zbl 1250.14026
[2] S.-T. Yau, Compact Three-Dimensional Kähler Manifolds with Zero Ricci Curvature, in Argonne/Chicago 1985, Proceedings, Anomalies, Geometry, Topology, (1986), pg. 395-406 [INSPIRE].
[3] Hubsch, T., Calabi-Yau manifolds: motivations and constructions, Commun. Math. Phys., 108, 291, (1987) · Zbl 0602.53061
[4] Green, P.; Hubsch, T., Calabi-Yau manifolds as complete intersections in products of complex projective spaces, Commun. Math. Phys., 109, 99, (1987) · Zbl 0611.53055
[5] Candelas, P.; Dale, AM; Lütken, CA; Schimmrigk, R., Complete intersection Calabi-Yau manifolds, Nucl. Phys., B 298, 493, (1988)
[6] P. Candelas, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds. 2. Three generation manifolds, Nucl. Phys.B 306 (1988) 113 [INSPIRE].
[7] Gray, J.; Haupt, AS; Lukas, A., All complete intersection Calabi-Yau four-folds, JHEP, 07, 070, (2013) · Zbl 1342.14086
[8] Gray, J.; Haupt, AS; Lukas, A., Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds, JHEP, 09, 093, (2014)
[9] Anderson, LB; Apruzzi, F.; Gao, X.; Gray, J.; Lee, S-J, A new construction of Calabi-Yau manifolds: generalized cicys, Nucl. Phys., B 906, 441, (2016) · Zbl 1334.14023
[10] Braun, V.; He, Y-H; Ovrut, BA; Pantev, T., A heterotic standard model, Phys. Lett., B 618, 252, (2005) · Zbl 1247.81349
[11] Braun, V.; He, Y-H; Ovrut, BA; Pantev, T., A standard model from the E_{8} × E_{8} heterotic superstring, JHEP, 06, 039, (2005)
[12] Bouchard, V.; Donagi, R., An SU(5) heterotic standard model, Phys. Lett., B 633, 783, (2006) · Zbl 1247.81348
[13] Braun, V.; Candelas, P.; Davies, R., A three-generation Calabi-Yau manifold with small Hodge numbers, Fortsch. Phys., 58, 467, (2010) · Zbl 1194.14061
[14] Braun, V.; Candelas, P.; Davies, R.; Donagi, R., The MSSM spectrum from (0, 2)-deformations of the heterotic standard embedding, JHEP, 05, 127, (2012) · Zbl 1348.81435
[15] Anderson, LB; He, Y-H; Lukas, A., Heterotic compactification, an algorithmic approach, JHEP, 07, 049, (2007)
[16] Anderson, LB; He, Y-H; Lukas, A., Monad bundles in heterotic string compactifications, JHEP, 07, 104, (2008)
[17] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., The edge of supersymmetry: stability walls in heterotic theory, Phys. Lett., B 677, 190, (2009)
[18] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Stability walls in heterotic theories, JHEP, 09, 026, (2009)
[19] Anderson, LB; Gray, J.; Ovrut, B., Yukawa textures from heterotic stability walls, JHEP, 05, 086, (2010) · Zbl 1287.81087
[20] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Stabilizing the complex structure in heterotic Calabi-Yau vacua, JHEP, 02, 088, (2011) · Zbl 1294.81153
[21] Anderson, LB; Gray, J.; Ovrut, BA, Transitions in the web of heterotic vacua, Fortsch. Phys., 59, 327, (2011) · Zbl 1215.81076
[22] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Stabilizing all geometric moduli in heterotic Calabi-Yau vacua, Phys. Rev., D 83, 106011, (2011) · Zbl 1294.81153
[23] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications, JHEP, 10, 032, (2011) · Zbl 1303.81139
[24] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Vacuum varieties, holomorphic bundles and complex structure stabilization in heterotic theories, JHEP, 07, 017, (2013) · Zbl 1342.81391
[25] Anderson, LB; Gray, J.; Grayson, D.; He, Y-H; Lukas, A., Yukawa couplings in heterotic compactification, Commun. Math. Phys., 297, 95, (2010) · Zbl 1203.81130
[26] Anderson, LB; Gray, J.; He, Y-H; Lukas, A., Exploring positive monad bundles and A new heterotic standard model, JHEP, 02, 054, (2010) · Zbl 1270.81146
[27] Anderson, LB; Gray, J.; Lukas, A.; Palti, E., Two hundred heterotic standard models onsmooth Calabi-Yau threefolds, Phys. Rev., D 84, 106005, (2011)
[28] Anderson, LB; Gray, J.; Lukas, A.; Palti, E., Heterotic line bundle standard models, JHEP, 06, 113, (2012) · Zbl 1397.81406
[29] Anderson, LB; Constantin, A.; Gray, J.; Lukas, A.; Palti, E., A comprehensive scan for heterotic SU(5) GUT models, JHEP, 01, 047, (2014)
[30] Buchbinder, EI; Constantin, A.; Lukas, A., The moduli space of heterotic line bundle models: a case study for the tetra-quadric, JHEP, 03, 025, (2014)
[31] Buchbinder, EI; Constantin, A.; Lukas, A., Non-generic couplings in supersymmetric standard models, Phys. Lett., B 748, 251, (2015) · Zbl 1345.81138
[32] Buchbinder, EI; Constantin, A.; Lukas, A., A heterotic standard model with B − L symmetry and a stable proton, JHEP, 06, 100, (2014) · Zbl 1390.81572
[33] Anderson, LB; Constantin, A.; Lee, S-J; Lukas, A., Hypercharge flux in heterotic compactifications, Phys. Rev., D 91, 046008, (2015)
[34] Buchbinder, EI; Constantin, A.; Lukas, A., Heterotic QCD axion, Phys. Rev., D 91, 046010, (2015)
[35] Groot Nibbelink, S.; Loukas, O.; Ruehle, F.; Vaudrevange, PKS, Infinite number of MSSMs from heterotic line bundles?, Phys. Rev., D 92, 046002, (2015)
[36] S. Groot Nibbelink, O. Loukas and F. Ruehle, (MS)SM-like models on smooth Calabi-Yau manifolds from all three heterotic string theories, Fortsch. Phys.63 (2015) 609 [arXiv:1507.07559] [INSPIRE]. · Zbl 1338.81337
[37] Constantin, A.; Lukas, A.; Mishra, C., The family problem: hints from heterotic line bundle models, JHEP, 03, 173, (2016) · Zbl 1388.81512
[38] Blesneag, S.; Buchbinder, EI; Candelas, P.; Lukas, A., Holomorphic Yukawa couplings in heterotic string theory, JHEP, 01, 152, (2016) · Zbl 1388.81776
[39] Buchbinder, EI; Constantin, A.; Gray, J.; Lukas, A., Yukawa unification in heterotic string theory, Phys. Rev., D 94, 046005, (2016)
[40] Blumenhagen, R.; Honecker, G.; Weigand, T., Loop-corrected compactifications of the heterotic string with line bundles, JHEP, 06, 020, (2005)
[41] Blumenhagen, R.; Moster, S.; Weigand, T., Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds, Nucl. Phys., B 751, 186, (2006) · Zbl 1192.81257
[42] Blumenhagen, R.; Moster, S.; Reinbacher, R.; Weigand, T., Massless spectra of three generation U(N) heterotic string vacua, JHEP, 05, 041, (2007)
[43] Candelas, P.; Davies, R., New Calabi-Yau manifolds with small Hodge numbers, Fortsch. Phys., 58, 383, (2010) · Zbl 1194.14062
[44] Candelas, P.; Constantin, A., Completing the web of Z_{3}-quotients of complete intersection Calabi-Yau manifolds, Fortsch. Phys., 60, 345, (2012) · Zbl 1243.81147
[45] Candelas, P.; Constantin, A.; Mishra, C., Hodge numbers for CICYs with symmetries of order divisible by 4, Fortsch. Phys., 64, 463, (2016) · Zbl 1339.14023
[46] P. Candelas, A. Constantin and C. Mishra, Calabi-Yau Threefolds With Small Hodge Numbers, arXiv:1602.06303 [INSPIRE].
[47] Gray, J.; He, Y-H; Ilderton, A.; Lukas, A., A new method for finding vacua in string phenomenology, JHEP, 07, 023, (2007)
[48] T. Hübsch, Calabi-Yau Manifolds: A Bestiary for Physicists, World Scientific (1994). · Zbl 1243.81147
[49] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley Classics Library, Wiley (2011). · Zbl 0408.14001
[50] J. Distler and B.R. Greene, Aspects of (2\(,\) 0) String Compactifications, Nucl. Phys.B 304 (1988) 1 [INSPIRE].
[51] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer (1977).
[52] The data for CICYs and their symmetries can be found at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/CicyQuotients/index.html.
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