Abstract
We develop methods to compute holomorphic Yukawa couplings for heterotic compactifications on complete intersection Calabi-Yau manifolds, generalising results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based on constructing the required bundle-valued forms explicitly and evaluating the relevant integrals over the projective ambient space. We also show how our approach relates to an earlier, algebraic one to calculate the holomorphic Yukawa couplings. A vanishing theorem, which we prove, implies that certain Yukawa couplings allowed by low-energy symmetries are zero due to topological reasons. To illustrate our methods, we calculate Yukawa couplings for SU(5)-based standard models on a co-dimension two complete intersection manifold.
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].
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].
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].
X. de la Ossa, E. Hardy and E.E. Svanes, The heterotic superpotential and moduli, JHEP 01 (2016) 049 [arXiv:1509.08724] [INSPIRE].
P. Candelas, X. de la Ossa and J. McOrist, A metric for heterotic moduli, arXiv:1605.05256 [INSPIRE].
J. McOrist, On the effective field theory of heterotic vacua, arXiv:1606.05221 [INSPIRE].
S. Blesneag, E.I. Buchbinder, P. Candelas and A. Lukas, Holomorphic Yukawa couplings in heterotic string theory, JHEP 01 (2016) 152 [arXiv:1512.05322] [INSPIRE].
P. Candelas, A.M. Dale, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys. B 298 (1988) 493 [INSPIRE].
P. Candelas, C.A. Lütken and R. Schimmrigk, Complete intersection Calabi-Yau manifolds. 2. Three generation manifolds, Nucl. Phys. B 306 (1988) 113 [INSPIRE].
V. Braun, On free quotients of complete intersection Calabi-Yau manifolds, JHEP 04 (2011) 005 [arXiv:1003.3235] [INSPIRE].
P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley Classics Library, U.S.A. (2011).
R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, Springer, Germany (1977).
D. Huybrechts, Complex geometry: an introduction, Springer, Germany (2005).
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: 1607.03461
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. & Lukas, A. Holomorphic Yukawa couplings for complete intersection Calabi-Yau manifolds. J. High Energ. Phys. 2017, 119 (2017). https://doi.org/10.1007/JHEP01(2017)119
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2017)119