Abstract
We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these techniques relate to algebraic methods for computing holomorphic Yukawa couplings. We apply our methods to various examples and evaluate the holomorphic Yukawa couplings explicitly as functions of the complex structure moduli. It is shown that the rank of the Yukawa matrix can decrease at specific loci in complex structure moduli space. In particular, we compute the up Yukawa coupling and the singlet-Higgs-lepton trilinear coupling in the heterotic standard model described in ref. [32].
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46 [INSPIRE].
A. Strominger and E. Witten, New manifolds for superstring compactification, Commun. Math. Phys. 101 (1985) 341 [INSPIRE].
E. Witten, Symmetry breaking patterns in superstring models, Nucl. Phys. B 258 (1985) 75 [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. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, The exact MSSM spectrum from string theory, JHEP 05 (2006) 043 [hep-th/0512177] [INSPIRE].
V. Bouchard and R. Donagi, An SU(5) heterotic standard model, Phys. Lett. B 633 (2006) 783 [hep-th/0512149] [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].
R. Blumenhagen, S. Moster, R. Reinbacher and T. Weigand, Massless spectra of three generation U(N) heterotic string vacua, JHEP 05 (2007) 041 [hep-th/0612039] [INSPIRE].
L.B. Anderson, Y.-H. He and A. Lukas, Heterotic compactification, an algorithmic approach, JHEP 07 (2007) 049 [hep-th/0702210] [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, 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 and R. Davies, A three-generation Calabi-Yau manifold with small Hodge numbers, Fortsch. Phys. 58 (2010) 467 [arXiv:0910.5464] [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].
A. Strominger, Yukawa couplings in superstring compactification, Phys. Rev. Lett. 55 (1985) 2547 [INSPIRE].
P. Candelas, Yukawa couplings between (2, 1) forms, Nucl. Phys. B 298 (1988) 458 [INSPIRE].
P. Candelas and X. de la Ossa, Moduli space of Calabi-Yau manifolds, Nucl. Phys. B 355 (1991) 455 [INSPIRE].
B.R. Greene, K.H. Kirklin, P.J. Miron and G.G. Ross, A three generation superstring model. 1. Compactification and discrete symmetries, Nucl. Phys. B 278 (1986) 667 [INSPIRE].
B.R. Greene, K.H. Kirklin, P.J. Miron and G.G. Ross, A three generation superstring model. 2. Symmetry breaking and the low-energy theory, Nucl. Phys. B 292 (1987) 606 [INSPIRE].
B.R. Greene, K.H. Kirklin, P.J. Miron and G.G. Ross, 273 Yukawa couplings for a three generation superstring model, Phys. Lett. B 192 (1987) 111 [INSPIRE].
V. Braun, Y.-H. He and B.A. Ovrut, Yukawa couplings in heterotic standard models, JHEP 04 (2006) 019 [hep-th/0601204] [INSPIRE].
V. Bouchard, M. Cvetič and R. Donagi, Tri-linear couplings in an heterotic minimal supersymmetric standard model, Nucl. Phys. B 745 (2006) 62 [hep-th/0602096] [INSPIRE].
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] [INSPIRE].
L.B. Anderson, J. Gray and B. Ovrut, Yukawa textures from heterotic stability walls, JHEP 05 (2010) 086 [arXiv:1001.2317] [INSPIRE].
P. Green and T. Hubsch, Calabi-Yau manifolds as complete intersections in products of complex projective spaces, Commun. Math. Phys. 109 (1987) 99 [INSPIRE].
P. Candelas, A.M. Dale, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys. B 298 (1988) 493 [INSPIRE].
T. Hubsch, Calabi-Yau manifolds: a bestiary for physicists, World Scientific, Singapore (1992) [INSPIRE].
E.I. Buchbinder, A. Constantin and A. Lukas, The moduli space of heterotic line bundle models: a case study for the tetra-quadric, JHEP 03 (2014) 025 [arXiv:1311.1941] [INSPIRE].
E.I. Buchbinder, A. Constantin and A. Lukas, A heterotic standard model with B-L symmetry and a stable proton, JHEP 06 (2014) 100 [arXiv:1404.2767] [INSPIRE].
E.I. Buchbinder, A. Constantin and A. Lukas, Non-generic couplings in supersymmetric standard models, Phys. Lett. B 748 (2015) 251 [arXiv:1409.2412] [INSPIRE].
E.I. Buchbinder, A. Constantin and A. Lukas, Heterotic QCD axion, Phys. Rev. D 91 (2015) 046010 [arXiv:1412.8696] [INSPIRE].
D. Huybrechts, Complex geometry: an introduction, Springer, Berlin Germany (2004).
M.B. Green, J.H. Schwarz and E. Witten, Supersting theory. Vol. 2: loop amplitudes, anomalies and phenomenology, Cambridge University Press, Cambridge U.K. (1987).
P. Candelas, Lectures on complex manifolds, published in Proceedings, Superstrings 87, Trieste Italy (1987), pg. 1 [INSPIRE].
P. Griffiths and J. Harris, Principles of algebraic geometry, Interscience, New York U.S.A. (1978).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1512.05322
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Blesneag, S., Buchbinder, E.I., Candelas, P. et al. Holomorphic Yukawa couplings in heterotic string theory. J. High Energ. Phys. 2016, 152 (2016). https://doi.org/10.1007/JHEP01(2016)152
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2016)152