Abstract
It has recently been realised that polystable, holomorphic sums of line bundles over smooth Calabi-Yau three-folds provide a fertile ground for heterotic model building. Large numbers of phenomenologically promising such models have been constructed for various classes of Calabi-Yau manifolds. In this paper we focus on a case study for the tetra-quadric—a Calabi-Yau hypersurface embedded in a product of four \( \mathbb{C}{{\mathbb{P}}^1} \) spaces. We address the question of finiteness of the class of consistent and physically viable line bundle models constructed on this manifold. Further, for a specific semi-realistic example, we explore the embedding of the line bundle sum into the larger moduli space of non-Abelian bundles, both by means of constructing specific polystable non-Abelian bundles and by turning on VEVs in the associated low-energy theory. In this context, we explore the fate of the Higgs doublets as we move in bundle moduli space. The non-Abelian compactifications thus constructed lead to SU(5) GUT models with an additional global B − L symmetry. The non-Abelian compactifications inherit many of the appealing phenomenological features of the Abelian model, such as the absence of dimension four and dimension five operators triggering fast proton decay.
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References
P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum Configurations for Superstrings, Nucl. Phys. B 258 (1985) 46 [INSPIRE].
V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, A heterotic standard model, Phys. Lett. B 618 (2005) 252 [hep-th/0501070] [INSPIRE].
V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, A standard model from the E 8 × E 8 heterotic superstring, JHEP 06 (2005) 039 [hep-th/0502155] [INSPIRE].
V. Bouchard and R. Donagi, An SU(5) heterotic standard model, Phys. Lett. B 633 (2006) 783 [hep-th/0512149] [INSPIRE].
L.B. Anderson, J. Gray, Y.-H. He and A. Lukas, Exploring Positive Monad Bundles And A New Heterotic Standard Model, JHEP 02 (2010) 054 [arXiv:0911.1569] [INSPIRE].
V. Braun, P. Candelas, R. Davies and R. Donagi, The MSSM Spectrum from (0, 2)-Deformations of the Heterotic Standard Embedding, JHEP 05 (2012) 127 [arXiv:1112.1097] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and E. Palti, Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds, Phys. Rev. D 84 (2011) 106005 [arXiv:1106.4804] [INSPIRE].
L.B. Anderson, J. Gray, A. Lukas and E. Palti, Heterotic Line Bundle Standard Models, JHEP 06 (2012) 113 [arXiv:1202.1757] [INSPIRE].
L.B. Anderson, A. Constantin, J. Gray, A. Lukas and E. Palti, A comprehensive Scan for Heterotic SU(5) GUT models, JHEP 01 (2014) 047 [arXiv:1307.4787] [INSPIRE].
Y.-H. He, S.-J. Lee, A. Lukas and C. Sun, Heterotic Model Building: 16 Special Manifolds, arXiv:1309.0223 [INSPIRE].
J. Distler and B.R. Greene, Aspects of (2, 0) String Compactifications, Nucl. Phys. B 304 (1988) 1 [INSPIRE].
R. Blumenhagen, G. Honecker and T. Weigand, Loop-corrected compactifications of the heterotic string with line bundles, JHEP 06 (2005) 020 [hep-th/0504232] [INSPIRE].
R. Blumenhagen, G. Honecker and T. Weigand, Supersymmetric (non-)Abelian bundles in the Type I and SO(32) heterotic string, JHEP 08 (2005) 009 [hep-th/0507041] [INSPIRE].
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].
L.B. Anderson, J. Gray and B.A. Ovrut, Transitions in the Web of Heterotic Vacua, Fortsch. Phys. 59 (2011) 327 [arXiv:1012.3179] [INSPIRE].
M. Kuriyama, H. Nakajima and T. Watari, Theoretical Framework for R-parity Violation, Phys. Rev. D 79 (2009) 075002 [arXiv:0802.2584] [INSPIRE].
L.B. Anderson, J. Gray and B. Ovrut, Yukawa Textures From Heterotic Stability Walls, JHEP 05 (2010) 086 [arXiv:1001.2317] [INSPIRE].
P. Candelas and R. Davies, New Calabi-Yau Manifolds with Small Hodge Numbers, Fortsch. Phys. 58 (2010) 383 [arXiv:0809.4681] [INSPIRE].
P. Candelas and A. Constantin, Completing the Web of Z 3 -Quotients of Complete Intersection Calabi-Yau Manifolds, Fortsch. Phys. 60 (2012) 345 [arXiv:1010.1878] [INSPIRE].
The database of line bundle models on the tetraquadric manifold, labelled by the CICY reference number 7862, can be found at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/linebundlemodels/index.html.
P. Candelas and X. de la Ossa, Moduli Space of Calabi-Yau Manifolds, Nucl. Phys. B 355 (1991) 455 [INSPIRE].
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] [INSPIRE].
L.B. Anderson, Y.-H. He and A. Lukas, Monad Bundles in Heterotic String Compactifications, JHEP 07 (2008) 104 [arXiv:0805.2875] [INSPIRE].
L.B. Anderson, Heterotic and M-theory Compactifications for String Phenomenology, arXiv:0808.3621 [INSPIRE].
L.B. Anderson, J. Gray, Y.-H. He, S.-J. Lee and A. Lukas, CICY package, based on methods described in arXiv:0911.1569, arXiv:0911.0865, arXiv:0805.2875, hep-th/0703249, hep-th/0702210.
L.B. Anderson, J. Gray, A. Lukas and B. Ovrut, Vacuum Varieties, Holomorphic Bundles and Complex Structure Stabilization in Heterotic Theories, JHEP 07 (2013) 017 [arXiv:1304.2704] [INSPIRE].
V. Braun, On Free Quotients of Complete Intersection Calabi-Yau Manifolds, JHEP 04 (2011) 005 [arXiv:1003.3235] [INSPIRE].
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ArXiv ePrint: 1311.1941
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Buchbinder, E.I., Constantin, A. & Lukas, A. The moduli space of heterotic line bundle models: a case study for the tetra-quadric. J. High Energ. Phys. 2014, 25 (2014). https://doi.org/10.1007/JHEP03(2014)025
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DOI: https://doi.org/10.1007/JHEP03(2014)025