Abstract
We investigate orbifold and smooth Calabi-Yau compactifications of the non-supersymmetric heterotic SO(16)×SO(16) string. We focus on such Calabi-Yau backgrounds in order to recycle commonly employed techniques, like index theorems and cohomology theory, to determine both the fermionic and bosonic 4D spectra. We argue that the N=0 theory never leads to tachyons on smooth Calabi-Yaus in the large volume approximation. As twisted tachyons may arise on certain singular orbifolds, we conjecture that such tachyonic states are lifted in the full blow-up. We perform model searches on selected orbifold geometries. In particular, we construct an explicit example of a Standard Model-like theory with three generations and a single Higgs field.
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].
V. Bouchard and R. Donagi, An SU(5) heterotic standard model, Phys. Lett. B 633 (2006) 783 [hep-th/0512149] [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].
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].
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on orbifolds, Nucl. Phys. B 261 (1985) 678 [INSPIRE].
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on orbifolds. 2., Nucl. Phys. B 274 (1986) 285 [INSPIRE].
L.E. Ibáñez, H.P. Nilles and F. Quevedo, Orbifolds and Wilson lines, Phys. Lett. B 187 (1987) 25 [INSPIRE].
L.E. Ibáñez, J. Mas, H.-P. Nilles and F. Quevedo, Heterotic strings in symmetric and asymmetric orbifold backgrounds, Nucl. Phys. B 301 (1988) 157 [INSPIRE].
D. Bailin and A. Love, Orbifold compactifications of string theory, Phys. Rept. 315 (1999) 285 [INSPIRE].
K.-S. Choi and J.E. Kim Quarks and leptons from orbifolded superstring, Springer, Heidelberg Germany (2006).
W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Supersymmetric standard model from the heterotic string, Phys. Rev. Lett. 96 (2006) 121602 [hep-ph/0511035] [INSPIRE].
W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Supersymmetric standard model from the heterotic string, Phys. Rev. Lett. 96 (2006) 121602 [hep-ph/0511035] [INSPIRE].
O. Lebedev et al., A mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett. B 645 (2007) 88 [hep-th/0611095] [INSPIRE].
O. Lebedev, H.P. Nilles, S. Ramos-Sánchez, M. Ratz and P.K.S. Vaudrevange, Heterotic mini-landscape. (II). Completing the search for MSSM vacua in a Z(6) orbifold, Phys. Lett. B 668 (2008) 331 [arXiv:0807.4384] [INSPIRE].
D.K. Mayorga Pena, H.P. Nilles and P.-K. Oehlmann, A Zip-code for Quarks, Leptons and Higgs Bosons, JHEP 12 (2012) 024 [arXiv:1209.6041] [INSPIRE].
J.E. Kim and B. Kyae, String MSSM through flipped SU(5) from Z(12) orbifold, hep-th/0608085 [INSPIRE].
J.E. Kim, J.-H. Kim and B. Kyae, Superstring standard model from Z(12 − I) orbifold compactification with and without exotics and effective R-parity, JHEP 06 (2007) 034 [hep-ph/0702278] [INSPIRE].
S. Groot Nibbelink and O. Loukas, MSSM-like models on Z(8) toroidal orbifolds, JHEP 12 (2013) 044 [arXiv:1308.5145] [INSPIRE].
H.P. Nilles and P.K.S. Vaudrevange, Geography of fields in extra dimensions: string theory lessons for particle physics, arXiv:1403.1597 [INSPIRE].
S. Groot Nibbelink, J. Held, F. Ruehle, M. Trapletti and P.K.S. Vaudrevange, Heterotic Z(6 − II) MSSM orbifolds in blowup, JHEP 03 (2009) 005 [arXiv:0901.3059] [INSPIRE].
M. Blaszczyk et al., A Z 2 × Z 2 standard model, Phys. Lett. B 683 (2010) 340 [arXiv:0911.4905] [INSPIRE].
M. Blaszczyk, S. Groot Nibbelink, F. Ruehle, M. Trapletti and P.K.S. Vaudrevange, Heterotic MSSM on a resolved orbifold, JHEP 09 (2010) 065 [arXiv:1007.0203] [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
K.R. Dienes, Modular invariance, finiteness and misaligned supersymmetry: new constraints on the numbers of physical string states, Nucl. Phys. B 429 (1994) 533 [hep-th/9402006] [INSPIRE].
K.R. Dienes, Statistics on the heterotic landscape: gauge groups and cosmological constants of four-dimensional heterotic strings, Phys. Rev. D 73 (2006) 106010 [hep-th/0602286] [INSPIRE].
G. Shiu and S.H.H. Tye, Bose-Fermi degeneracy and duality in nonsupersymmetric strings, Nucl. Phys. B 542 (1999) 45 [hep-th/9808095] [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, Classification of closed fermionic string models, Phys. Rev. D 34 (1986) 3794 [INSPIRE].
J.D. Blum and K.R. Dienes, Duality without supersymmetry: the case of the SO(16) × SO(16) string, Phys. Lett. B 414 (1997) 260 [hep-th/9707148] [INSPIRE].
A.E. Faraggi and M. Tsulaia, On the low energy spectra of the nonsupersymmetric heterotic string theories, Eur. Phys. J. C 54 (2008) 495 [arXiv:0706.1649] [INSPIRE].
W. Lerche, D. Lüst and A.N. Schellekens, Ten-dimensional heterotic strings from Niemeier lattices, Phys. Lett. B 181 (1986) 71 [INSPIRE].
W. Lerche, D. Lüst and A.N. Schellekens, Chiral four-dimensional heterotic strings from selfdual lattices, Nucl. Phys. B 287 (1987) 477 [INSPIRE].
J. Held, D. Lüst, F. Marchesano and L. Martucci, DWSB in heterotic flux compactifications, JHEP 06 (2010) 090 [arXiv:1004.0867] [INSPIRE].
A. Sagnotti, Some properties of open string theories, hep-th/9509080 [INSPIRE].
A. Sagnotti, Surprises in open string perturbation theory, Nucl. Phys. Proc. Suppl. 56B (1997) 332 [hep-th/9702093] [INSPIRE].
C. Angelantonj, Nontachyonic open descendants of the 0B string theory, Phys. Lett. B 444 (1998) 309 [hep-th/9810214] [INSPIRE].
S. Sugimoto, Anomaly cancellations in type-I d9 − d9 system and the USp(32) string theory, Prog. Theor. Phys. 102 (1999) 685 [hep-th/9905159] [INSPIRE].
R. Blumenhagen, A. Font and D. Lüst, Tachyon free orientifolds of type 0B strings in various dimensions, Nucl. Phys. B 558 (1999) 159 [hep-th/9904069] [INSPIRE].
G. Aldazabal, L.E. Ibáñez and F. Quevedo, Standard-like models with broken supersymmetry from type-I string vacua, JHEP 01 (2000) 031 [hep-th/9909172] [INSPIRE].
S. Moriyama, USp(32) string as spontaneously supersymmetry broken theory, Phys. Lett. B 522 (2001) 177 [hep-th/0107203] [INSPIRE].
B. Gato-Rivera and A.N. Schellekens, Non-supersymmetric Tachyon-free Type-II and Type-I closed strings from RCFT, Phys. Lett. B 656 (2007) 127 [arXiv:0709.1426] [INSPIRE].
B. Gato-Rivera and A.N. Schellekens, Non-supersymmetric orientifolds of Gepner models, Phys. Lett. B 671 (2009) 105 [arXiv:0810.2267] [INSPIRE].
L.J. Dixon and J.A. Harvey, String theories in ten-dimensions without space-time supersymmetry, Nucl. Phys. B 274 (1986) 93 [INSPIRE].
L. Álvarez-Gaumé, P.H. Ginsparg, G.W. Moore and C. Vafa, An O(16) × O(16) heterotic string, Phys. Lett. B 171 (1986) 155 [INSPIRE].
K.S. Narain, M.H. Sarmadi and E. Witten, A note on toroidal compactification of heterotic string theory, Nucl. Phys. B 279 (1987) 369 [INSPIRE].
K.S. Narain, New heterotic string theories in uncompactified dimensions < 10, Phys. Lett. B 169 (1986) 41 [INSPIRE].
V.P. Nair, A.D. Shapere, A. Strominger and F. Wilczek, Compactification of the twisted heterotic string, Nucl. Phys. B 287 (1987) 402 [INSPIRE].
P.H. Ginsparg and C. Vafa, Toroidal compactification of nonsupersymmetric heterotic strings, Nucl. Phys. B 289 (1987) 414 [INSPIRE].
D. Lüst, Compactification of the O(16) × O(16) heterotic string theory, Phys. Lett. B 178 (1986) 174 [INSPIRE].
W. Fischler and L. Susskind, Dilaton tadpoles, string condensates and scale invariance, Phys. Lett. B 171 (1986) 383 [INSPIRE].
W. Fischler and L. Susskind, Dilaton tadpoles, string condensates and scale invariance. 2., Phys. Lett. B 173 (1986) 262 [INSPIRE].
T.R. Taylor, Model building on asymmetric Z(3) orbifolds: nonsupersymmetric models, Nucl. Phys. B 303 (1988) 543 [INSPIRE].
A. Toon, Nonsupersymmetric Z(4) orbifolds and Atkin-Lehner symmetry, Phys. Lett. B 243 (1990) 68 [INSPIRE].
T. Sasada, Asymmetric orbifold models of nonsupersymmetric heterotic strings, Prog. Theor. Phys. 95 (1996) 249 [hep-th/9508098] [INSPIRE].
A. Font and A. Hernandez, Nonsupersymmetric orbifolds, Nucl. Phys. B 634 (2002) 51 [hep-th/0202057] [INSPIRE].
D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, Heterotic string theory. 1. The free heterotic string, Nucl. Phys. B 256 (1985) 253 [INSPIRE].
D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, Heterotic string theory. 2. The interacting heterotic string, Nucl. Phys. B 267 (1986) 75 [INSPIRE].
R. Rohm, Spontaneous supersymmetry breaking in supersymmetric string theories, Nucl. Phys. B 237 (1984) 553 [INSPIRE].
L.E. Ibáñez, J. Mas, H.-P. Nilles and F. Quevedo, Heterotic strings in symmetric and asymmetric orbifold backgrounds, Nucl. Phys. B 301 (1988) 157 [INSPIRE].
A. Font, L.E. Ibáñez, H.P. Nilles and F. Quevedo, Degenerate orbifolds, Nucl. Phys. B 307 (1988) 109 [Erratum ibid. B 310 (1988) 764] [INSPIRE].
F. Plöger, S. Ramos-Sánchez, M. Ratz and P.K.S. Vaudrevange, Mirage torsion, JHEP 04 (2007) 063 [hep-th/0702176] [INSPIRE].
J.A. Casas, E.K. Katehou and C. Muñoz, U(1) charges in orbifolds: anomaly cancellation and phenomenological consequences, Nucl. Phys. B 317 (1989) 171 [INSPIRE].
M.B. Green, J.H. Schwarz and E. Witten Superstring theory. Vol. 2: Loop amplitudes, anomalies and phenomenology, Cambridge Monographs On Mathematical Physics, Cambridge University Press, Cambridge U.K. (1987).
S. Groot Nibbelink, M. Trapletti and M. Walter, Resolutions of C n /Z n orbifolds, their U(1) bundles, and applications to string model building, JHEP 03 (2007) 035 [hep-th/0701227] [INSPIRE].
S. Groot Nibbelink, T.-W. Ha and M. Trapletti, Toric resolutions of heterotic orbifolds, Phys. Rev. D 77 (2008) 026002 [arXiv:0707.1597] [INSPIRE].
R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, The spectra of heterotic standard model vacua, JHEP 06 (2005) 070 [hep-th/0411156] [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].
S. Groot Nibbelink, Blowups of heterotic orbifolds using toric geometry, arXiv:0708.1875 [INSPIRE].
S. Groot Nibbelink, D. Klevers, F. Ploger, M. Trapletti and P.K.S. Vaudrevange, Compact heterotic orbifolds in blow-up, JHEP 04 (2008) 060 [arXiv:0802.2809] [INSPIRE].
D. Lüst, S. Reffert, E. Scheidegger and S. Stieberger, Resolved toroidal orbifolds and their orientifolds, Adv. Theor. Math. Phys. 12 (2008) 67 [hep-th/0609014] [INSPIRE].
S. Reffert, The geometer’s toolkit to string compactifications, arXiv:0706.1310 [INSPIRE].
M. Blaszczyk, S. Groot Nibbelink and F. Ruehle, Gauged linear σ-models for toroidal orbifold resolutions, JHEP 05 (2012) 053 [arXiv:1111.5852] [INSPIRE].
S. Groot Nibbelink, H.P. Nilles and M. Trapletti, Multiple anomalous U(1)s in heterotic blow-ups, Phys. Lett. B 652 (2007) 124 [hep-th/0703211] [INSPIRE].
H.P. Nilles, S. Ramos-Sánchez, P.K.S. Vaudrevange and A. Wingerter, The Orbifolder: a tool to study the low energy effective theory of heterotic orbifolds, Comput. Phys. Commun. 183 (2012) 1363 [arXiv:1110.5229] [INSPIRE].
M. Fischer, M. Ratz, J. Torrado and P.K.S. Vaudrevange, Classification of symmetric toroidal orbifolds, JHEP 01 (2013) 084 [arXiv:1209.3906] [INSPIRE].
S. Ramos-Sánchez, Towards Low Energy Physics from the Heterotic String, Fortsch. Phys. 10 (2009) 907 [arXiv:0812.3560] [INSPIRE].
E. Dudas and J. Mourad, Brane solutions in strings with broken supersymmetry and dilaton tadpoles, Phys. Lett. B 486 (2000) 172 [hep-th/0004165] [INSPIRE].
E. Dudas, J. Mourad and C. Timirgaziu, Time and space dependent backgrounds from nonsupersymmetric strings, Nucl. Phys. B 660 (2003) 3 [hep-th/0209176] [INSPIRE].
S. Kachru, J. Kumar and E. Silverstein, Vacuum energy cancellation in a nonsupersymmetric string, Phys. Rev. D 59 (1999) 106004 [hep-th/9807076] [INSPIRE].
G.W. Moore, Atkin-Lehner symmetry, Nucl. Phys. B 293 (1987) 139 [Erratum ibid. B 299 (1988) 847] [INSPIRE].
K.R. Dienes, Generalized Atkin-Lehner symmetry, Phys. Rev. D 42 (1990) 2004 [INSPIRE].
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: 1407.6362
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
Blaszczyk, M., Nibbelink, S.G., Loukas, O. et al. Non-supersymmetric heterotic model building. J. High Energ. Phys. 2014, 119 (2014). https://doi.org/10.1007/JHEP10(2014)119
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2014)119