zbMATH — the first resource for mathematics

The MSSM spectrum from $$(0,2)$$-deformations of the heterotic standard embedding. (English) Zbl 1348.81435
Summary: We construct supersymmetric compactifications of $$E_8\times E_8$$ heterotic string theory which realise exactly the massless spectrum of the Minimal Supersymmetric Standard Model (MSSM) at low energies. The starting point is the standard embedding on a CalabiYau threefold which has Hodge numbers $$(h^{1,1}, h^{2,1}) = (1, 4)$$ and fundamental group $$\mathbb{Z}^{12}$$, which gives an $$E_6$$ grand unified theory with three net chiral generations. The gauge symmetry is then broken to that of the standard model by a combination of discrete Wilson lines and continuous deformation of the gauge bundle. On eight distinct branches of the moduli space, we find stable bundles with appropriate cohomology groups to give exactly the massless spectrum of the MSSM.

MSC:
 81T70 Quantization in field theory; cohomological methods 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T60 Supersymmetric field theories in quantum mechanics
Full Text:
References:
 [1] Candelas, P.; Horowitz, GT; Strominger, A.; Witten, E., Vacuum configurations for superstrings, Nucl. Phys., B 258, 46, (1985) [2] Greene, BR; Kirklin, KH; Miron, PJ; Ross, GG, A three generation superstring model. 2. symmetry breaking and the low-energy theory, Nucl. Phys., B 292, 606, (1987) [3] Donaldson, SK, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, P. Lond. Math. Soc., 50, 1, (1985) [4] Uhlenbeck, K.; Yau, ST, On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Commun. Pur. Appl. Math., 39, 257, (1986) [5] Braun, V.; He, Y-H; Ovrut, BA, Stability of the minimal heterotic standard model bundle, JHEP, 06, 032, (2006) [6] Anderson, LB; He, Y-H; Lukas, A., Monad bundles in heterotic string compactifications, JHEP, 07, 104, (2008) [7] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., The edge of supersymmetry: stability walls in heterotic theory, Phys. Lett., B 677, 190, (2009) [8] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Stability walls in heterotic theories, JHEP, 09, 026, (2009) [9] Bouchard, V.; Donagi, R., An SU(5) heterotic standard model, Phys. Lett., B 633, 783, (2006) [10] Anderson, LB; Gray, J.; Lukas, A.; Palti, E., Two hundred heterotic standard models on smooth Calabi-Yau threefolds, Phys. Rev., D 84, 106005, (2011) [11] Braun, V.; He, Y-H; Ovrut, BA; Pantev, T., The exact MSSM spectrum from string theory, JHEP, 05, 043, (2006) [12] Bouchard, V.; Donagi, R., On heterotic model constraints, JHEP, 08, 060, (2008) [13] Anderson, LB; Gray, J.; He, Y-H; Lukas, A., Exploring positive monad bundles and A new heterotic standard model, JHEP, 02, 054, (2010) [14] J. McOrist and I.V. Melnikov, Old issues and linear σ-models, arXiv:1103.1322 [INSPIRE]. [15] Braun, V.; Candelas, P.; Davies, R., A three-generation Calabi-Yau manifold with small Hodge numbers, Fortsch. Phys., 58, 467, (2010) [16] Braun, V., On free quotients of complete intersection Calabi-Yau manifolds, JHEP, 04, 005, (2011) [17] J. Li and S.-T. Yau, The Existence of supersymmetric string theory with torsion, hep-th/0411136 [INSPIRE]. [18] R. Donagi, R. Reinbacher and S.-T. Yau, Yukawa couplings on quintic threefolds, hep-th/0605203 [INSPIRE]. [19] McInnes, B., Group theoretic aspects of the hosotani mechanism, J. Phys., A 22, 2309, (1989) [20] Donagi, R.; Ovrut, BA; Pantev, T.; Reinbacher, R., SU(4) instantons on Calabi-Yau threefolds with Z(2) × Z(2) fundamental group, JHEP, 01, 022, (2004) [21] Batyrev, VV, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom., 3, 493, (1994) [22] Kreuzer, M.; Skarke, H., Complete classification of reflexive polyhedra in four-dimensions, Adv. Theor. Math. Phys., 4, 1209, (2002) [23] Aspinwall, PS; Greene, BR; Morrison, DR, Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory, Nucl. Phys., B 416, 414, (1994) [24] V. Bouchard, Lectures on complex geometry, Calabi-Yau manifolds and toric geometry, hep-th/0702063 [INSPIRE]. [25] K. Hori et al., Mirror symmetry, AMS (2003). [26] W. Fulton, Introduction to Toric Varieties, Princeton University Press, Princeton (1993). [27] D. A. Cox, J. B. Little and H. K. Schenck, Toric Varieties, AMS (2011). [28] Candelas, P.; Dale, A.; Lütken, C.; Schimmrigk, R., Complete intersection Calabi-Yau manifolds, Nucl. Phys., B 298, 493, (1988) [29] Candelas, P.; Lütken, C.; Schimmrigk, R., Complete intersection Calabi-Yau manifolds. 2. three generation manifolds, Nucl. Phys., B 306, 113, (1988) [30] Candelas, P.; Davies, R., New Calabi-Yau manifolds with small Hodge numbers, Fortsch. Phys., 58, 383, (2010) [31] D.A. Cox, The Homogeneous coordinate ring of a toric variety, revised version, alg-geom/9210008 [INSPIRE]. [32] J. Distler, Notes on (0, 2) superconformal field theories, hep-th/9502012 [INSPIRE]. [33] Witten, E., Symmetry breaking patterns in superstring models, Nucl. Phys., B 258, 75, (1985) [34] Witten, E., New issues in manifolds of SU(3) holonomy, Nucl. Phys., B 268, 79, (1986) [35] Kreuzer, M.; McOrist, J.; Melnikov, IV; Plesser, MR, (0, 2) deformations of linear σ-models, JHEP, 07, 044, (2011) [36] Davies, R., The expanding zoo of Calabi-Yau threefolds, Adv. High Energy Phys., 2011, 901898, (2011) [37] S.T. Yau, Compact three-dimensional Kähler manifolds with zero Ricci curvature, in proceedings of Symposium on Anomalies, Geometry, Topology, Argonne/Chicago (1985) 395. [38] Candelas, P.; Ossa, X.; He, Y-H; Szendroi, B., Triadophilia: A special corner in the landscape, Adv. Theor. Math. Phys., 12, 2, (2008) [39] Anderson, LB; He, Y-H; Lukas, A., Heterotic compactification, an algorithmic approach, JHEP, 07, 049, (2007) [40] L.B. Anderson, Heterotic and M-theory Compactifications for String Phenomenology, arXiv:0808.3621 [INSPIRE]. [41] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer (1977).
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.