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Calabi-Yau compactifications of non-supersymmetric heterotic string theory. (English) Zbl 1388.81491

Summary: Phenomenological explorations of heterotic strings have conventionally focused primarily on the \(E_{8}\times E_{8}\) theory. We consider smooth compactifications of all three ten-dimensional heterotic theories to exhibit the many similarities between the non-supersymmetric \(\mathrm{SO}(16)\times SO(16)\) theory and the related supersymmetric \(E_{8}\times E_{8}\) and \(\mathrm{SO}(32)\) theories. In particular, we exploit these similarities to determine the bosonic and fermionic spectra of Calabi-Yau compactifications with line bundles of the non-supersymmetric string. We use elements of four-dimensional supersymmetric effective field theory to characterize the non-supersymmetric action at leading order and determine the Green-Schwarz induced axion couplings. Using these methods we construct a non-supersymmetric Standard Model(SM)-like theory. In addition, we show that it is possible to obtain SM-like models from the standard embedding using at least an order four Wilson line. Finally, we make a proposal of the states that live on five-branes in the \(\mathrm{SO}(16)\times SO(16)\) theory and find under certain assumptions the surprising result that anomaly factorization only admits at most a single brane solution.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory

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[1] L.J. Dixon and J.A. Harvey, String theories in ten-dimensions without space-time supersymmetry, Nucl. Phys.B 274 (1986) 93 [INSPIRE]. · doi:10.1016/0550-3213(86)90619-X
[2] L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on orbifolds. 2., Nucl. Phys.B 274 (1986) 285 [INSPIRE]. · doi:10.1016/0550-3213(86)90287-7
[3] 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]. · doi:10.1016/0370-2693(86)91524-8
[4] R. Rohm, Spontaneous supersymmetry breaking in supersymmetric string theories, Nucl. Phys.B 237 (1984) 553 [INSPIRE]. · doi:10.1016/0550-3213(84)90007-5
[5] C. Kounnas and B. Rostand, Coordinate Dependent Compactifications and Discrete Symmetries, Nucl. Phys.B 341 (1990) 641 [INSPIRE]. · doi:10.1016/0550-3213(90)90543-M
[6] D. Kutasov and N. Seiberg, Number of degrees of freedom, density of states and tachyons in string theory and CFT, Nucl. Phys.B 358 (1991) 600 [INSPIRE]. · doi:10.1016/0550-3213(91)90426-X
[7] J.A. Harvey, String duality and nonsupersymmetric strings, Phys. Rev.D 59 (1999) 026002 [hep-th/9807213] [INSPIRE].
[8] V.P. Nair, A.D. Shapere, A. Strominger and F. Wilczek, Compactification of the twisted heterotic string, Nucl. Phys.B 287 (1987) 402 [INSPIRE]. · doi:10.1016/0550-3213(87)90112-X
[9] P.H. Ginsparg and C. Vafa, Toroidal compactification of nonsupersymmetric heterotic strings, Nucl. Phys.B 289 (1987) 414 [INSPIRE]. · doi:10.1016/0550-3213(87)90387-7
[10] W. Lerche, D. Lüst and A.N. Schellekens, Ten-dimensional heterotic strings from Niemeier lattices, Phys. Lett.B 181 (1986) 71 [INSPIRE]. · doi:10.1016/0370-2693(86)91257-8
[11] W. Lerche, D. Lüst and A.N. Schellekens, Chiral four-dimensional heterotic strings from selfdual lattices, Nucl. Phys.B 287 (1987) 477 [INSPIRE]. · doi:10.1016/0550-3213(87)90115-5
[12] L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on orbifolds, Nucl. Phys.B 261 (1985) 678 [INSPIRE]. · doi:10.1016/0550-3213(85)90593-0
[13] L.E. Ibáñez, H.P. Nilles and F. Quevedo, Orbifolds and Wilson lines, Phys. Lett.B 187 (1987) 25 [INSPIRE]. · doi:10.1016/0370-2693(87)90066-9
[14] 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]. · doi:10.1016/0550-3213(88)90166-6
[15] T.R. Taylor, Model building on asymmetric Z(3) orbifolds: Nonsupersymmetric models, Nucl. Phys.B 303 (1988) 543 [INSPIRE]. · doi:10.1016/0550-3213(88)90393-8
[16] A. Toon, Nonsupersymmetric Z(4) orbifolds and Atkin-Lehner symmetry, Phys. Lett.B 243 (1990) 68 [INSPIRE]. · doi:10.1016/0370-2693(90)90958-9
[17] T. Sasada, Asymmetric orbifold models of nonsupersymmetric heterotic strings, Prog. Theor. Phys.95 (1996) 249 [hep-th/9508098] [INSPIRE]. · doi:10.1143/PTP.95.249
[18] A. Font and A. Hernández, Nonsupersymmetric orbifolds, Nucl. Phys.B 634 (2002) 51 [hep-th/0202057] [INSPIRE]. · Zbl 0995.83059 · doi:10.1016/S0550-3213(02)00336-X
[19] H. Kawai, D.C. Lewellen and S.H.H. Tye, Classification of closed fermionic string models, Phys. Rev.D 34 (1986) 3794 [INSPIRE].
[20] I. Antoniadis, C.P. Bachas and C. Kounnas, Four-Dimensional Superstrings, Nucl. Phys.B 289 (1987) 87 [INSPIRE]. · doi:10.1016/0550-3213(87)90372-5
[21] I. Antoniadis and C. Bachas, 4 − D Fermionic Superstrings with Arbitrary Twists, Nucl. Phys.B 298 (1988) 586 [INSPIRE]. · doi:10.1016/0550-3213(88)90355-0
[22] 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]. · Zbl 1020.81768 · doi:10.1016/0550-3213(94)90153-8
[23] 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]. · doi:10.1016/S0370-2693(97)01172-6
[24] 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]. · Zbl 0942.81055 · doi:10.1016/S0550-3213(98)00775-5
[25] 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].
[26] 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]. · Zbl 1189.81177 · doi:10.1140/epjc/s10052-008-0545-2
[27] C. Angelantonj, I. Antoniadis and K. Forger, Nonsupersymmetric type-I strings with zero vacuum energy, Nucl. Phys.B 555 (1999) 116 [hep-th/9904092] [INSPIRE]. · Zbl 0955.81051 · doi:10.1016/S0550-3213(99)00344-2
[28] C. Angelantonj, I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti, Type I vacua with brane supersymmetry breaking, Nucl. Phys.B 572 (2000) 36 [hep-th/9911081] [INSPIRE]. · Zbl 0947.81124 · doi:10.1016/S0550-3213(00)00052-3
[29] C. Angelantonj and E. Dudas, Metastable string vacua, Phys. Lett.B 651 (2007) 239 [arXiv:0704.2553] [INSPIRE]. · Zbl 1248.83126 · doi:10.1016/j.physletb.2007.06.031
[30] A. Sagnotti, Some properties of open string theories, hep-th/9509080 [INSPIRE]. · Zbl 1043.83034
[31] A. Sagnotti, Surprises in open string perturbation theory, Nucl. Phys. Proc. Suppl.56B (1997) 332 [hep-th/9702093] [INSPIRE]. · Zbl 0925.81138 · doi:10.1016/S0920-5632(97)00344-7
[32] C. Angelantonj, Nontachyonic open descendants of the 0B string theory, Phys. Lett.B 444 (1998) 309 [hep-th/9810214] [INSPIRE]. · doi:10.1016/S0370-2693(98)01430-0
[33] I. Antoniadis, E. Dudas and A. Sagnotti, Brane supersymmetry breaking, Phys. Lett.B 464 (1999) 38 [hep-th/9908023] [INSPIRE]. · Zbl 0987.81551 · doi:10.1016/S0370-2693(99)01023-0
[34] S. Sugimoto, Anomaly cancellations in type-ID‐9‐D¯‐\[9 D\hbox{-} 9\hbox{-} \overline{D}\hbox{-} 9\] system and the USp(32) string theory, Prog. Theor. Phys.102 (1999) 685 [hep-th/9905159] [INSPIRE]. · doi:10.1143/PTP.102.685
[35] 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]. · Zbl 1068.81584 · doi:10.1016/S0550-3213(99)00381-8
[36] G. Aldazabal and A.M. Uranga, Tachyon free nonsupersymmetric type IIB orientifolds via brane-anti-brane systems, JHEP10 (1999) 024 [hep-th/9908072] [INSPIRE]. · Zbl 0957.81040 · doi:10.1088/1126-6708/1999/10/024
[37] G. Aldazabal, L.E. Ibáñez and F. Quevedo, Standard-like models with broken supersymmetry from type-I string vacua, JHEP01 (2000) 031 [hep-th/9909172] [INSPIRE]. · Zbl 0990.81721 · doi:10.1088/1126-6708/2000/01/031
[38] 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]. · Zbl 1050.81640 · doi:10.1016/S0370-2693(00)00734-6
[39] S. Moriyama, USp(32) string as spontaneously supersymmetry broken theory, Phys. Lett.B 522 (2001) 177 [hep-th/0107203] [INSPIRE]. · Zbl 0973.81105 · doi:10.1016/S0370-2693(01)01278-3
[40] 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]. · Zbl 1034.81038 · doi:10.1016/S0550-3213(03)00248-7
[41] 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]. · Zbl 1246.81246 · doi:10.1016/j.physletb.2007.09.009
[42] B. Gato-Rivera and A.N. Schellekens, Non-supersymmetric orientifolds of Gepner models, Phys. Lett.B 671 (2009) 105 [arXiv:0810.2267] [INSPIRE]. · doi:10.1016/j.physletb.2008.11.039
[43] M. Blaszczyk, S. Groot Nibbelink, O. Loukas and S. Ramos-Sanchez, Non-supersymmetric heterotic model building, JHEP10 (2014) 119 [arXiv:1407.6362] [INSPIRE]. · Zbl 1333.81315 · doi:10.1007/JHEP10(2014)119
[44] S.G. Nibbelink, Model building with the non-supersymmetric heterotic SO(16) × SO(16) string, J. Phys. Conf. Ser.631 (2015) 012077 [arXiv:1502.03604] [INSPIRE]. · doi:10.1088/1742-6596/631/1/012077
[45] A. Lukas, Z. Lalak and E.E. Svanes, Heterotic moduli stabilisation and non-supersymmetric vacua, JHEP08 (2015) 020 [arXiv:1504.06978] [INSPIRE]. · Zbl 1388.81577 · doi:10.1007/JHEP08(2015)020
[46] S. Abel, K.R. Dienes and E. Mavroudi, Towards a nonsupersymmetric string phenomenology, Phys. Rev.D 91 (2015) 126014 [arXiv:1502.03087] [INSPIRE].
[47] J.M. Ashfaque, P. Athanasopoulos, A.E. Faraggi and H. Sonmez, Non-Tachyonic Semi-Realistic Non-Supersymmetric Heterotic String Vacua, arXiv:1506.03114 [INSPIRE].
[48] H. Itoyama and T.R. Taylor, Supersymmetry Restoration in the Compactified O(16) × O(16)-prime Heterotic String Theory, Phys. Lett.B 186 (1987) 129 [INSPIRE]. · doi:10.1016/0370-2693(87)90267-X
[49] K.R. Dienes, New string partition functions with vanishing cosmological constant, Phys. Rev. Lett.65 (1990) 1979 [INSPIRE]. · doi:10.1103/PhysRevLett.65.1979
[50] A.E. Faraggi and M. Tsulaia, Interpolations Among NAHE-based Supersymmetric and Nonsupersymmetric String Vacua, Phys. Lett.B 683 (2010) 314 [arXiv:0911.5125] [INSPIRE]. · doi:10.1016/j.physletb.2009.12.039
[51] C. Angelantonj, I. Florakis and M. Tsulaia, Universality of Gauge Thresholds in Non-Supersymmetric Heterotic Vacua, Phys. Lett.B 736 (2014) 365 [arXiv:1407.8023] [INSPIRE]. · Zbl 1317.81157 · doi:10.1016/j.physletb.2014.08.001
[52] I. Florakis, Universality of radiative corrections to gauge couplings for strings with spontaneously broken supersymmetry, J. Phys. Conf. Ser.631 (2015) 012079 [arXiv:1502.07537] [INSPIRE]. · doi:10.1088/1742-6596/631/1/012079
[53] C.M. Hull and E. Witten, Supersymmetric σ-models and the Heterotic String, Phys. Lett.B 160 (1985) 398 [INSPIRE]. · doi:10.1016/0370-2693(85)90008-5
[54] C.M. Hull, Complex structures and isometries in the (2,0) supersymmetric nonlinear σ-model, Mod. Phys. Lett.A 5 (1990) 1793 [INSPIRE]. · Zbl 1020.81846 · doi:10.1142/S0217732390002043
[55] R. Blumenhagen, G. Honecker and T. Weigand, Loop-corrected compactifications of the heterotic string with line bundles, JHEP06 (2005) 020 [hep-th/0504232] [INSPIRE]. · doi:10.1088/1126-6708/2005/06/020
[56] R. Blumenhagen, G. Honecker and T. Weigand, Supersymmetric (non-)Abelian bundles in the Type I and SO(32) heterotic string, JHEP08 (2005) 009 [hep-th/0507041] [INSPIRE]. · doi:10.1088/1126-6708/2005/08/009
[57] 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]. · Zbl 1192.81257 · doi:10.1016/j.nuclphysb.2006.06.005
[58] 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]. · Zbl 1247.81349 · doi:10.1016/j.physletb.2005.05.007
[59] V. Bouchard and R. Donagi, An SU(5) heterotic standard model, Phys. Lett.B 633 (2006) 783 [hep-th/0512149] [INSPIRE]. · Zbl 1247.81348 · doi:10.1016/j.physletb.2005.12.042
[60] L.B. Anderson, Y.-H. He and A. Lukas, Heterotic compactification, an algorithmic approach, JHEP07 (2007) 049 [hep-th/0702210] [INSPIRE]. · doi:10.1088/1126-6708/2007/07/049
[61] S. Groot Nibbelink, M. Trapletti and M. Walter, Resolutions of Cn/Znorbifolds, their U(1) bundles and applications to string model building, JHEP03 (2007) 035 [hep-th/0701227] [INSPIRE]. · doi:10.1088/1126-6708/2007/03/035
[62] S. Groot Nibbelink, J. Held, F. Ruehle, M. Trapletti and P.K.S. Vaudrevange, Heterotic Z(6-II) MSSM orbifolds in blowup, JHEP03 (2009) 005 [arXiv:0901.3059] [INSPIRE]. · doi:10.1088/1126-6708/2009/03/005
[63] M. Blaszczyk, S. Groot Nibbelink, F. Ruehle, M. Trapletti and P.K.S. Vaudrevange, Heterotic MSSM on a resolved orbifold, JHEP09 (2010) 065 [arXiv:1007.0203] [INSPIRE]. · Zbl 1291.81296 · doi:10.1007/JHEP09(2010)065
[64] 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].
[65] L.B. Anderson, J. Gray, A. Lukas and E. Palti, Heterotic line bundle Standard Models, JHEP06 (2012) 113 [arXiv:1202.1757] [INSPIRE]. · Zbl 1397.81406 · doi:10.1007/JHEP06(2012)113
[66] P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys.B 258 (1985) 46 [INSPIRE]. · doi:10.1016/0550-3213(85)90602-9
[67] A. Strominger, Superstrings with torsion, Nucl. Phys.B 274 (1986) 253 [INSPIRE]. · doi:10.1016/0550-3213(86)90286-5
[68] P. Candelas, A.M. Dale, C.A. Lütken and R. Schimmrigk, Complete Intersection Calabi-Yau Manifolds, Nucl. Phys.B 298 (1988) 493 [INSPIRE]. · doi:10.1016/0550-3213(88)90352-5
[69] CALABI-YAU Home Page: A resource for information about Calabi-Yau manifolds, http://www.th.physik.uni-bonn.de/Supplements/cy.html (1996).
[70] V. Braun, On Free Quotients of Complete Intersection Calabi-Yau Manifolds, JHEP04 (2011) 005 [arXiv:1003.3235] [INSPIRE]. · Zbl 1250.14026 · doi:10.1007/JHEP04(2011)005
[71] M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett.B 149 (1984) 117 [INSPIRE]. · doi:10.1016/0370-2693(84)91565-X
[72] M.B. Green, J.H. Schwarz and P.C. West, Anomaly free chiral theories in six-dimensions, Nucl. Phys.B 254 (1985) 327 [INSPIRE]. · doi:10.1016/0550-3213(85)90222-6
[73] 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). · Zbl 0619.53002
[74] N. Marcus, A. Sagnotti and W. Siegel, Ten-dimensional Supersymmetric Yang-Mills Theory in Terms of Four-dimensional Superfields, Nucl. Phys.B 224 (1983) 159 [INSPIRE]. · doi:10.1016/0550-3213(83)90318-8
[75] N. Arkani-Hamed, T. Gregoire and J.G. Wacker, Higher dimensional supersymmetry in 4 − D superspace, JHEP03 (2002) 055[hep-th/0101233] [INSPIRE]. · doi:10.1088/1126-6708/2002/03/055
[76] G. Lopes Cardoso, G. Curio, G. Dall’Agata, D. Lüst, P. Manousselis and G. Zoupanos, Non-Kähler string backgrounds and their five torsion classes, Nucl. Phys.B 652 (2003) 5 [hep-th/0211118] [INSPIRE]. · Zbl 1010.83063 · doi:10.1016/S0550-3213(03)00049-X
[77] K. Becker, M. Becker, K. Dasgupta and P.S. Green, Compactifications of heterotic theory on nonKähler complex manifolds. 1., JHEP04 (2003) 007 [hep-th/0301161] [INSPIRE]. · doi:10.1088/1126-6708/2003/04/007
[78] J.P. Gauntlett, D. Martelli and D. Waldram, Superstrings with intrinsic torsion, Phys. Rev.D 69 (2004) 086002 [hep-th/0302158] [INSPIRE].
[79] K. Becker, M. Becker, P.S. Green, K. Dasgupta and E. Sharpe, Compactifications of heterotic strings on nonKähler complex manifolds. 2., Nucl. Phys.B 678 (2004) 19 [hep-th/0310058] [INSPIRE]. · Zbl 1097.81703 · doi:10.1016/j.nuclphysb.2003.11.029
[80] K. Becker, M. Becker, J.-X. Fu, L.-S. Tseng and S.-T. Yau, Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory, Nucl. Phys.B 751 (2006) 108 [hep-th/0604137] [INSPIRE]. · Zbl 1192.81312 · doi:10.1016/j.nuclphysb.2006.05.034
[81] M. Fernandez, S. Ivanov, L. Ugarte and R. Villacampa, Non-Kähler Heterotic String Compactifications with non-zero fluxes and constant dilaton, Commun. Math. Phys.288 (2009) 677 [arXiv:0804.1648] [INSPIRE]. · Zbl 1197.83103 · doi:10.1007/s00220-008-0714-z
[82] M. Klaput, A. Lukas, C. Matti and E.E. Svanes, Moduli stabilising in heterotic nearly Káhler compactifications, JHEP01 (2013) 015 [arXiv:1210.5933] [INSPIRE]. · Zbl 1342.81443 · doi:10.1007/JHEP01(2013)015
[83] S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, Nucl. Phys.B 433 (1995) 501 [hep-th/9406055] [INSPIRE]. · Zbl 1020.32508 · doi:10.1016/0550-3213(94)00440-P
[84] A. Lukas and K.S. Stelle, Heterotic anomaly cancellation in five-dimensions, JHEP01 (2000) 010 [hep-th/9911156] [INSPIRE]. · Zbl 0989.81595 · doi:10.1088/1126-6708/2000/01/010
[85] S. Groot Nibbelink, T.-W. Ha and M. Trapletti, Toric resolutions of heterotic orbifolds, Phys. Rev.D 77 (2008) 026002 [arXiv:0707.1597] [INSPIRE].
[86] S. Groot Nibbelink, D. Klevers, F. Ploger, M. Trapletti and P.K.S. Vaudrevange, Compact heterotic orbifolds in blow-up, JHEP04 (2008) 060 [arXiv:0802.2809] [INSPIRE]. · Zbl 1246.81251 · doi:10.1088/1126-6708/2008/04/060
[87] M. Nakahara, Geometry, topology and physics, Graduate Student Series in Physics, Adam Hilger, Bristol U.K. (1990). · Zbl 0764.53001
[88] G. Honecker, Massive U(1)s and heterotic five-branes on K3, Nucl. Phys.B 748 (2006) 126 [hep-th/0602101] [INSPIRE]. · Zbl 1186.81103 · doi:10.1016/j.nuclphysb.2006.04.027
[89] R. Blumenhagen, B. Jurke, T. Rahn and H. Roschy, Cohomology of Line Bundles: A Computational Algorithm, J. Math. Phys.51 (2010) 103525 [arXiv:1003.5217] [INSPIRE]. · Zbl 1314.55012 · doi:10.1063/1.3501132
[90] cohomCalg package, High-performance line bundle cohomology computation based on [89], http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg/ (2010).
[91] E. Witten, Dimensional Reduction of Superstring Models, Phys. Lett.B 155 (1985) 151 [INSPIRE]. · doi:10.1016/0370-2693(85)90976-1
[92] J.P. Derendinger, L.E. Ibáñez and H.P. Nilles, On the Low-Energy Limit of Superstring Theories, Nucl. Phys.B 267 (1986) 365 [INSPIRE]. · doi:10.1016/0550-3213(86)90396-2
[93] S. Ferrara, C. Kounnas and M. Porrati, General Dimensional Reduction of Ten-Dimensional Supergravity and Superstring, Phys. Lett.B 181 (1986) 263 [INSPIRE]. · doi:10.1016/0370-2693(86)90043-2
[94] L.J. Dixon, V. Kaplunovsky and J. Louis, On Effective Field Theories Describing (2,2) Vacua of the Heterotic String, Nucl. Phys.B 329 (1990) 27 [INSPIRE]. · doi:10.1016/0550-3213(90)90057-K
[95] A. Strominger, Yukawa couplings in superstring compactification, Phys. Rev. Lett.55 (1985) 2547 [INSPIRE]. · doi:10.1103/PhysRevLett.55.2547
[96] E. Witten, Symmetry Breaking Patterns in Superstring Models, Nucl. Phys.B 258 (1985) 75 [INSPIRE]. · doi:10.1016/0550-3213(85)90603-0
[97] K.-S. Choi, K. Hwang and J.E. Kim, Dynkin diagram strategy for orbifolding with Wilson lines, Nucl. Phys.B 662 (2003) 476 [hep-th/0304243] [INSPIRE]. · Zbl 1034.81521 · doi:10.1016/S0550-3213(03)00308-0
[98] N. Seiberg and E. Witten, Comments on string dynamics in six-dimensions, Nucl. Phys.B 471 (1996) 121 [hep-th/9603003] [INSPIRE]. · Zbl 1003.81535 · doi:10.1016/0550-3213(96)00189-7
[99] L.B. Anderson, A. Constantin, J. Gray, A. Lukas and E. Palti, A comprehensive scan for heterotic SU(5) GUT models, JHEP01 (2014) 047 [arXiv:1307.4787] [INSPIRE]. · doi:10.1007/JHEP01(2014)047
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.