Heterotic bundles on Calabi-Yau manifolds with small Picard number. (English) Zbl 1306.81246
Summary: We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, we construct positive rank five monad bundles over Calabi-Yau hypersurfaces in toric varieties, with the number of Kähler moduli equal to one, two, and three and extract physically interesting models. We select models which can lead to three families of matter after dividing by a freely-acting discrete symmetry and including Wilson lines. About 2000 such models on two manifolds are found.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81R60 | Noncommutative geometry in quantum theory |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
Software:
PALPReferences:
| [1] | P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys.B 258 (1985) 46 [INSPIRE]. · doi:10.1016/0550-3213(85)90602-9 |
| [2] | M. Kreuzer and H. Skarke, On the classification of reflexive polyhedra, Commun. Math. Phys.185 (1997) 495 [hep-th/9512204] [INSPIRE]. · Zbl 0894.14026 · doi:10.1007/s002200050100 |
| [3] | A. Avram, M. Kreuzer, M. Mandelberg and H. Skarke, The web of Calabi-Yau hypersurfaces in toric varieties, Nucl. Phys.B 505 (1997) 625 [hep-th/9703003] [INSPIRE]. · Zbl 0896.14026 · doi:10.1016/S0550-3213(97)00582-8 |
| [4] | M. Kreuzer and H. Skarke, Reflexive polyhedra, weights and toric Calabi-Yau fibrations, Rev. Math. Phys.14 (2002) 343 [math/0001106] [INSPIRE]. · Zbl 1079.14534 · doi:10.1142/S0129055X0200120X |
| [5] | M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four-dimensions, Adv. Theor. Math. Phys.4 (2002) 1209 [hep-th/0002240] [INSPIRE]. · Zbl 1017.52007 |
| [6] | M. Kreuzer and H. Skarke, PALP: a package for analyzing lattice polytopes with applications to toric geometry, Comput. Phys. Commun.157 (2004) 87 [math/0204356] [INSPIRE]. · Zbl 1196.14007 · doi:10.1016/S0010-4655(03)00491-0 |
| [7] | L.B. Anderson, J. Gray, A. Lukas and E. Palti, Two hundred heterotic standard models on smooth Calabi-Yau threefolds, arXiv:1106.4804 [INSPIRE]. |
| [8] | L.B. Anderson, Y.-H. He and A. Lukas, Monad bundles in heterotic string compactifications, JHEP07 (2008) 104 [arXiv:0805.2875] [INSPIRE]. · doi:10.1088/1126-6708/2008/07/104 |
| [9] | L.B. Anderson, J. Gray, Y.-H. He and A. Lukas, Exploring positive monad bundles and a new heterotic standard model, JHEP02 (2010) 054 [arXiv:0911.1569] [INSPIRE]. · Zbl 1270.81146 · doi:10.1007/JHEP02(2010)054 |
| [10] | L.B. Anderson, Y.-H. He and A. Lukas, Heterotic compactification, an algorithmic approach, JHEP07 (2007) 049 [hep-th/0702210] [INSPIRE]. · doi:10.1088/1126-6708/2007/07/049 |
| [11] | P. Candelas, A. Dale, C. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys.B 298 (1988) 493 [INSPIRE]. · doi:10.1016/0550-3213(88)90352-5 |
| [12] | M. Gabella, Y.-H. He and A. Lukas, An abundance of heterotic vacua, JHEP12 (2008) 027 DOI:dx.doi.org [arXiv:0808.2142] [INSPIRE]. · Zbl 1329.81313 · doi:dx.doi.org |
| [13] | V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, The exact MSSM spectrum from string theory, JHEP05 (2006) 043 [hep-th/0512177] [INSPIRE]. · doi:10.1088/1126-6708/2006/05/043 |
| [14] | V. Bouchard and R. Donagi, An SU(5) heterotic standard model, Phys. Lett.B 633 (2006) 783 [hep-th/0512149] [INSPIRE]. · Zbl 1247.81348 |
| [15] | Y.-H. He, S.-J. Lee and A. Lukas, Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds, JHEP05 (2010) 071 [arXiv:0911.0865] [INSPIRE]. · Zbl 1287.81094 · doi:10.1007/JHEP05(2010)071 |
| [16] | P. Candelas, X. de la Ossa, Y.-H. He and B. Szendroi, Triadophilia: a special corner in the landscape, Adv. Theor. Math. Phys.12 (2008) 2 [arXiv:0706.3134] [INSPIRE]. |
| [17] | V. Braun, P. Candelas and R. Davies, A three-generation Calabi-Yau manifold with small Hodge numbers, Fortsch. Phys.58 (2010) 467 [arXiv:0910.5464] [INSPIRE]. · Zbl 1194.14061 · doi:10.1002/prop.200900106 |
| [18] | P. Candelas and R. Davies, New Calabi-Yau manifolds with small Hodge numbers, Fortsch. Phys.58 (2010) 383 [arXiv:0809.4681] [INSPIRE]. · Zbl 1194.14062 · doi:10.1002/prop.200900105 |
| [19] | V. Braun, The 24-cell and Calabi-Yau threefolds with Hodge numbers (1,1), arXiv:1102.4880 [INSPIRE]. · Zbl 1348.14104 |
| [20] | A.P. Braun and N.-O. Walliser, A new offspring of PALP, arXiv:1106.4529 [INSPIRE]. |
| [21] | Y.-H. He, S.-J. Lee and A. Lukas, Positive monad bundles on toric Calabi-Yau hypersurfaces, http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/toricdata/index.html. |
| [22] | V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom.3 (1994) 493 [INSPIRE]. · Zbl 0829.14023 |
| [23] | G. Horrocks and D. Mumford, A rank 2 vector bundle on P4with 15000 symmetries, Topology 12 (1973) 63. · Zbl 0255.14017 · doi:10.1016/0040-9383(73)90022-0 |
| [24] | A. Beilinson, Coherent sheaves on Pnand problems in linear algebra, Funktsional. Anal. i Prilozhen. 12 (1978) 68. · Zbl 0402.14006 · doi:10.1007/BF01681436 |
| [25] | M. Maruyama, Moduli of stable sheaves, II, J. Math. Kyoto Univ. 18-3 (1978) 557. · Zbl 0395.14006 |
| [26] | C. Okonek, M. Schneider, H. Spindler, Vector bundles on complex projective spaces, Birkhauser Verlag, Berlin Germany (1988). · Zbl 1237.14003 |
| [27] | J. Distler and B.R. Greene, Aspects of (2, 0) string compactifications, Nucl. Phys.B 304 (1988)1 [INSPIRE]. · doi:10.1016/0550-3213(88)90619-0 |
| [28] | S. Kachru, Some three generation (0,2) Calabi-Yau models, Phys. Lett.B 349 (1995) 76 [hep-th/9501131] [INSPIRE]. |
| [29] | R. Blumenhagen, Target space duality for (0,2) compactifications, Nucl. Phys.B 513 (1998) 573 [hep-th/9707198] [INSPIRE]. · Zbl 0939.32017 · doi:10.1016/S0550-3213(97)00721-9 |
| [30] | R. Blumenhagen, R. Schimmrigk and A. Wisskirchen, (0,2) mirror symmetry, Nucl. Phys.B 486 (1997)598 [hep-th/9609167] [INSPIRE]. · Zbl 0925.14014 · doi:10.1016/S0550-3213(96)00698-0 |
| [31] | M.R. Douglas and C.-g. Zhou, Chirality change in string theory, JHEP06 (2004) 014 [hep-th/0403018] [INSPIRE]. · doi:10.1088/1126-6708/2004/06/014 |
| [32] | M. Chiara Brambilla, Semistability of certain bundles on a quintic Calabi-Yau threefold, math/0509599 . · Zbl 1161.14031 |
| [33] | R. Blumenhagen, S. Moster and T. Weigand, Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds, Nucl. Phys.B 751 (2006) 186 [hep-th/0603015] [INSPIRE]. · Zbl 1192.81257 · doi:10.1016/j.nuclphysb.2006.06.005 |
| [34] | R. Blumenhagen, S. Moster, R. Reinbacher and T. Weigand, Massless spectra of three generation U(N ) heterotic string vacua, JHEP05 (2007) 041 [hep-th/0612039] [INSPIRE]. · doi:10.1088/1126-6708/2007/05/041 |
| [35] | R. Hartshorne, Algebraic Geometry, Graduate text in mathematics, 52, Springer-Verlag, New York U.S.A. (1977). · Zbl 0367.14001 |
| [36] | P. Candelas, C. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds. 2. Three generation manifolds, Nucl. Phys.B 306 (1988) 113 [INSPIRE]. · doi:10.1016/0550-3213(88)90173-3 |
| [37] | L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stability walls in heterotic theories, JHEP09 (2009) 026 [arXiv:0905.1748] [INSPIRE]. · doi:10.1088/1126-6708/2009/09/026 |
| [38] | R. Blumenhagen, B. Jurke, T. Rahn and H. Roschy, Cohomology of line bundles: a computational algorithm, J. Math. Phys.51 (2010) 103525 [arXiv:1003.5217] [INSPIRE]. · Zbl 1314.55012 · doi:10.1063/1.3501132 |
| [39] | B. McInnes, Group theoretic aspects of the Hosotani mechanism, J. Phys.A 22 (1989) 2309 [INSPIRE]. · Zbl 0693.53008 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
