zbMATH — the first resource for mathematics

Heterotic models from vector bundles on toric Calabi-Yau manifolds. (English) Zbl 1287.81094
Summary: We systematically approach the construction of heterotic \(E_{8}\times E_{8}\) 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.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V25 Other elementary particle theory in quantum theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
Full Text: DOI arXiv
[1] Anderson, LB; He, Y-H; Lukas, A., Heterotic compactification, an algorithmic approach, JHEP, 07, 049, (2007)
[2] Anderson, LB; He, Y-H; Lukas, A., Monad bundles in heterotic string compactifications, JHEP, 07, 104, (2008)
[3] Gabella, M.; He, Y-H; Lukas, A., An abundance of heterotic vacua, JHEP, 12, 027, (2008)
[4] Anderson, LB; Gray, J.; Grayson, D.; He, Y-H; Lukas, A., Yukawa couplings in heterotic compactification, Commun. Math. Phys., 297, 95, (2010)
[5] C. Okonek, M. Schneider and H. Spindler, Vector bundles on complex projective spaces, Birkhauser Verlag, Boston U.S.A. (1988).
[6] Distler, J.; Greene, BR, Aspects of (2, 0) string compactifications, Nucl. Phys., B 304, 1, (1988)
[7] Kachru, S., Some three generation (0, 2) Calabi-Yau models, Phys. Lett., B 349, 76, (1995)
[8] Blumenhagen, R., Target space duality for (0, 2) compactifications, Nucl. Phys., B 513, 573, (1998)
[9] Blumenhagen, R.; Schimmrigk, R.; Wisskirchen, A., (0, 2) mirror symmetry, Nucl. Phys., B 486, 598, (1997)
[10] Douglas, MR; Zhou, C-G, Chirality change in string theory, JHEP, 06, 014, (2004)
[11] Candelas, P.; Dale, AM; Lütken, CA; Schimmrigk, R., Complete intersection Calabi-Yau manifolds, Nucl. Phys., B 298, 493, (1988)
[12] Candelas, P.; Lütken, CA; Schimmrigk, R., Complete intersection Calabi-Yau manifolds. 2: three generation manifolds, Nucl. Phys., B 306, 113, (1988)
[13] Green, PS; Hubsch, T.; Lütken, CA, All Hodge numbers of all complete intersection Calabi-Yau manifolds, Class. Quant. Grav., 6, 105, (1989)
[14] He, A-M; Candelas, P., On the number of complete intersection Calabi-Yau manifolds, Commun. Math. Phys., 135, 193, (1990)
[15] Gagnon, M.; Ho-Kim, Q., An exhaustive List of complete intersection Calabi-Yau manifolds, Mod. Phys. Lett., A 9, 2235, (1994)
[16] Candelas, P.; Horowitz, GT; Strominger, A.; Witten, E., Vacuum configurations for superstrings, Nucl. Phys., B 258, 46, (1985)
[17] Witten, E., New issues in manifolds of SU(3) holonomy, Nucl. Phys., B 268, 79, (1986)
[18] M.B. Green, J.H. Schwarz and E. Witten, Superstring theory, volume II, Cambridge University Press, Cambridge U.K. (1987) [SPIRES].
[19] Donagi, R.; He, Y-H; Ovrut, BA; Reinbacher, R., The particle spectrum of heterotic compactifications, JHEP, 12, 054, (2004)
[20] He, Y-H, GUT particle spectrum from heterotic compactification, Mod. Phys. Lett., A 20, 1483, (2005)
[21] Kreuzer, M.; Skarke, H., On the classification of reflexive polyhedra, Commun. Math. Phys., 185, 495, (1997)
[22] Kreuzer, M.; Skarke, H., Complete classification of reflexive polyhedra in four dimensions, Adv. Theor. Math. Phys., 4, 1209, (2002)
[23] Kreuzer, M.; Skarke, H., Refkexive polyhedra, weights and toric Calabi-Yau fibrations, Rev. Math. Phys., 14, 343, (2002)
[24] Kreuzer, M., Strings on Calabi-Yau spaces and toric geometry, Nucl. Phys. (Proc. Suppl.), 102, 87, (2001)
[25] M. Kreuzer, Toric geometry and Calabi-Yau compactifications, hep-th/0612307 [SPIRES].
[26] Kreuzer, M.; Riegler, E.; Sahakyan, DA, Toric complete intersections and weighted projective space, J. Geom. Phys., 46, 159, (2003)
[27] M. Kreuzer and B. Nill, Classification of toric Fano 5-folds, math.AG/0702890 [SPIRES].
[28] W. Fulton, Introduction to toric varieties, Princeton University Press, Princeton U.S.A. (1993).
[29] T. Oda, Convex bodies and algebraic geometry, Springer-Verlag, Germany (1988).
[30] D. Cox, Recent developments in toric geometry, alg-geom/9606016.
[31] V. Bouchard, Lectures on complex geometry, Calabi-Yau manifolds and toric geometry, hep-th/0702063 [SPIRES].
[32] Candelas, P.; Ossa, X.; He, Y-H; Szendroi, B., Triadophilia: a special corner in the landscape, Adv. Theor. Math. Phys., 12, 2, (2008)
[33] V. Braun, P. Candelas and R. Davies, A three-generation Calabi-Yau manifold with small Hodge numbers, arXiv:0910.5464 [SPIRES].
[34] Batyrev, VV, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom., 3, 493, (1994)
[35] Fulton, W.; Lazarsfeld, R., On the connectedness of degeneracy loci and special divisors, Acta Math., 146, 271, (1981)
[36] K. Hori at al., Mirror symmetry, American Mathematical Society, Providence U.S.A. (2003) [SPIRES].
[37] Aspinwall, PS; Greene, BR; Morrison, DR, Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory, Nucl. Phys., B 416, 414, (1994)
[38] D. Cox and S. Katz, Mirror symmetry and algebraic geometry, American Mathematical Society, Providence U.S.A. (1999) [SPIRES].
[39] Reid, M., Decomposition of toric morphisms, No. 36, 395, (1983), Boston U.S.A., Basel Switzerland and Berlin Germany
[40] Kreuzer, M.; Skarke, H., PALP: a package for analyzing lattice polytopes with applications to toric geometry, Comput. Phys. Commun., 157, 87, (2004)
[41] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., The edge of supersymmetry: stability walls in heterotic theory, Phys. Lett., B 677, 190, (2009)
[42] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Stability walls in heterotic theories, JHEP, 09, 026, (2009)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.