Abstract
We systematically approach the construction of heterotic E 8 × E 8 Calabi-Yau models, based on compact Calabi-Yau three-folds arising from toric geometry and vector bundles on these manifolds. We focus on a simple class of 101 such three-folds with smooth ambient spaces, on which we perform an exhaustive scan and find all positive monad bundles with SU(N), N = 3; 4; 5 structure groups, subject to the heterotic anomaly cancellation constraint. We find that anomaly-free positive monads exist on only 11 of these toric three-folds with a total number of bundles of about 2000. Only 21 of these models, all of them on three-folds realizable as hypersurfaces in products of projective spaces, allow for three families of quarks and leptons. We also perform a preliminary scan over the much larger class of semi-positive monads which leads to about 44000 bundles with 280 of them satisfying the three-family constraint. These 280 models provide a starting point for heterotic model building based on toric three-folds.
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L.B. Anderson, Y.-H. He and A. Lukas, Heterotic compactification, an algorithmic approach, JHEP 07 (2007) 049 [hep-th/0702210] [SPIRES].
L.B. Anderson, Y.-H. He and A. Lukas, Monad bundles in heterotic string compactifications, JHEP 07 (2008) 104 [arXiv:0805.2875] [SPIRES].
M. Gabella, Y.-H. He and A. Lukas, An abundance of heterotic vacua, JHEP 12 (2008) 027 [arXiv:0808.2142] [SPIRES].
L.B. Anderson, J. Gray, D. Grayson, Y.-H. He and A. Lukas, Yukawa couplings in heterotic compactification, Commun. Math. Phys. 297 (2010) 95 [arXiv:0904.2186] [SPIRES].
C. Okonek, M. Schneider and H. Spindler, Vector bundles on complex projective spaces, Birkhauser Verlag, Boston U.S.A. (1988).
J. Distler and B.R. Greene, Aspects of (2, 0) string compactifications, Nucl. Phys. B 304 (1988) 1 [SPIRES].
S. Kachru, Some three generation (0, 2) Calabi-Yau models, Phys. Lett. B 349 (1995) 76 [hep-th/9501131] [SPIRES].
R. Blumenhagen, Target space duality for (0, 2) compactifications, Nucl. Phys. B 513 (1998) 573 [hep-th/9707198] [SPIRES].
R. Blumenhagen, R. Schimmrigk and A. Wisskirchen, (0, 2) mirror symmetry, Nucl. Phys. B 486 (1997) 598 [hep-th/9609167] [SPIRES].
M.R. Douglas and C.-G. Zhou, Chirality change in string theory, JHEP 06 (2004) 014 [hep-th/0403018] [SPIRES].
P. Candelas, A.M. Dale, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys. B 298 (1988) 493 [SPIRES].
P. Candelas, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds. 2: Three generation manifolds, Nucl. Phys. B 306 (1988) 113 [SPIRES].
P.S. Green, T. Hubsch and C.A. Lütken, All Hodge numbers of all complete intersection Calabi-Yau manifolds, Class. Quant. Grav. 6 (1989) 105 [SPIRES].
A.-M. He and P. Candelas, On the number of complete intersection Calabi-Yau manifolds, Commun. Math. Phys. 135 (1990) 193 [SPIRES].
M. Gagnon and Q. Ho-Kim, An exhaustive list of complete intersection Calabi-Yau manifolds, Mod. Phys. Lett. A 9 (1994) 2235 [SPIRES].
P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46 [SPIRES].
E. Witten, New issues in manifolds of SU(3) holonomy, Nucl. Phys. B 268 (1986) 79 [SPIRES].
M.B. Green, J.H. Schwarz and E. Witten, Superstring theory, volume II, Cambridge University Press, Cambridge U.K. (1987) [SPIRES].
R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, The particle spectrum of heterotic compactifications, JHEP 12 (2004) 054 [hep-th/0405014] [SPIRES].
Y.-H. He, GUT particle spectrum from heterotic compactification, Mod. Phys. Lett. A 20 (2005) 1483 [SPIRES].
M. Kreuzer and H. Skarke, On the classification of reflexive polyhedra, Commun. Math. Phys. 185 (1997) 495 [hep-th/9512204] [SPIRES].
M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four dimensions, Adv. Theor. Math. Phys. 4 (2002) 1209 [hep-th/0002240] [SPIRES].
M. Kreuzer and H. Skarke, Refkexive polyhedra, weights and toric Calabi-Yau fibrations, Rev. Math. Phys. 14 (2002) 343 [math.AG/0001106] [SPIRES].
M. Kreuzer, Strings on Calabi-Yau spaces and toric geometry, Nucl. Phys. (Proc. Suppl.) 102 (2001) 87 [hep-th/0103243] [SPIRES].
M. Kreuzer, Toric geometry and Calabi-Yau compactifications, hep-th/0612307 [SPIRES].
M. Kreuzer, E. Riegler and D.A. Sahakyan, Toric complete intersections and weighted projective space, J. Geom. Phys. 46 (2003) 159 [math.AG/0103214] [SPIRES].
M. Kreuzer and B. Nill, Classification of toric Fano 5-folds, math.AG/0702890 [SPIRES].
W. Fulton, Introduction to toric varieties, Princeton University Press, Princeton U.S.A. (1993).
T. Oda, Convex bodies and algebraic geometry, Springer-Verlag, Germany (1988).
D. Cox, Recent developments in toric geometry, alg-geom/9606016.
V. Bouchard, Lectures on complex geometry, Calabi-Yau manifolds and toric geometry, hep-th/0702063 [SPIRES].
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] [SPIRES].
V. Braun, P. Candelas and R. Davies, A three-generation Calabi-Yau manifold with small Hodge numbers, arXiv:0910.5464 [SPIRES].
V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994) 493 [alg-geom/9310003] [SPIRES].
W. Fulton and R. Lazarsfeld, On the connectedness of degeneracy loci and special divisors, Acta Math. 146 (1981) 271.
K. Hori at al., Mirror symmetry, American Mathematical Society, Providence U.S.A. (2003) [SPIRES].
P.S. Aspinwall, B.R. Greene and D.R. Morrison, Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory, Nucl. Phys. B 416 (1994) 414 [hep-th/9309097] [SPIRES].
D. Cox and S. Katz, Mirror symmetry and algebraic geometry, American Mathematical Society, Providence U.S.A. (1999) [SPIRES].
M. Reid, Decomposition of toric morphisms, in Arithmetic and geometry, Progress in Mathematics 36, Birkhauser, Boston U.S.A., Basel Switzerland and Berlin Germany (1983), pg. 395.
M. Kreuzer and H. Skarke, PALP: a Package for Analyzing Lattice Polytopes with applications to toric geometry, Comput. Phys. Commun. 157 (2004) 87 [math.NA/0204356] [SPIRES].
L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, The edge of supersymmetry: stability walls in heterotic theory, Phys. Lett. B 677 (2009) 190 [arXiv:0903.5088] [SPIRES].
L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, Stability walls in heterotic theories, JHEP 09 (2009) 026 [arXiv:0905.1748] [SPIRES].
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ArXiv ePrint: 0911.0865
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He, YH., Lee, SJ. & Lukas, A. Heterotic models from vector bundles on toric Calabi-Yau manifolds. J. High Energ. Phys. 2010, 71 (2010). https://doi.org/10.1007/JHEP05(2010)071
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DOI: https://doi.org/10.1007/JHEP05(2010)071