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On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds. (English) Zbl 1214.81231
Summary: We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering \(all\) the bulk moduli, we obtain the 4D low energy effective action for the compactification, which has contributions from various, computable, perturbative and non-perturbative effects. Hidden sector gaugino condensation and string worldsheet instantons result in a combination of racetrack, KKLT-like and cusp-form contributions to the superpotential, which lift all the bulk moduli directions. We point out the properties observed in our concrete models, which tend to be missed when only “generic” features of a model are assumed. We search for interesting vacua and find several de Sitter solutions, but so far, they all turn out to be unstable.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
83E15 Kaluza-Klein and other higher-dimensional theories
81V22 Unified quantum theories
14J10 Families, moduli, classification: algebraic theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
57R18 Topology and geometry of orbifolds
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References:
[1] Cascales, JFG; García del Moral, MP; Quevedo, F.; Uranga, AM, Realistic D-brane models on warped throats: fluxes, hierarchies and moduli stabilization, JHEP, 02, 031, (2004)
[2] Marchesano, F.; Shiu, G., Building MSSM flux vacua, JHEP, 11, 041, (2004)
[3] Conlon, JP; Maharana, A.; Quevedo, F., Towards realistic string vacua, JHEP, 05, 109, (2009)
[4] Buchmüller, W.; Hamaguchi, K.; Lebedev, O.; Ratz, M., Supersymmetric standard model from the heterotic string, Phys. Rev. Lett., 96, 121602, (2006)
[5] Buchmüller, W.; Hamaguchi, K.; Lebedev, O.; Ratz, M., Supersymmetric standard model from the heterotic string. II, Nucl. Phys., B 785, 149, (2007)
[6] Lebedev, O.; etal., A mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett., B 645, 88, (2007)
[7] Lebedev, O.; etal., The heterotic road to the MSSM with R parity, Phys. Rev., D 77, 046013, (2008)
[8] Lebedev, O.; Nilles, HP; Ramos-Sánchez, S.; Ratz, M.; Vaudrevange, PKS, Heterotic mini-landscape (II): completing the search for MSSM vacua in a \(Z\)_{6} orbifold, Phys. Lett., B 668, 331, (2008)
[9] Dixon, LJ; Friedan, D.; Martinec, EJ; Shenker, SH, The conformal field theory of orbifolds, Nucl. Phys., B 282, 13, (1987)
[10] Bailin, D.; Love, A., Orbifold compactifications of string theory, Phys. Rept., 315, 285, (1999)
[11] K.-S. Choi and J.E. Kim, Quarks and Leptons From Orbifolded Superstring, Lecture Notes on Physics696, Springer, Heidelberg Germany (2006).
[12] Hamidi, S.; Vafa, C., Interactions on orbifolds, Nucl. Phys., B 279, 465, (1987)
[13] Dixon, LJ; Friedan, D.; Martinec, EJ; Shenker, SH, The conformal field theory of orbifolds, Nucl. Phys., B 282, 13, (1987)
[14] Dixon, LJ; Kaplunovsky, V.; Louis, J., On effective field theories describing (2, 2) vacua of the heterotic string, Nucl. Phys., B 329, 27, (1990)
[15] Ferrara, S.; Lüst, D.; Shapere, AD; Theisen, S., Modular invariance in supersymmetric field theories, Phys. Lett., B 225, 363, (1989)
[16] Lauer, J.; Mas, J.; Nilles, HP, Duality and the role of nonperturbative effects on the world sheet, Phys. Lett., B 226, 251, (1989)
[17] Lauer, J.; Mas, J.; Nilles, HP, Twisted sector representations of discrete background symmetries for two-dimensional orbifolds, Nucl. Phys., B 351, 353, (1991)
[18] Ibáñez, LE; Lüst, D., Duality anomaly cancellation, minimal string unification and the effective low-energy Lagrangian of 4 − D strings, Nucl. Phys., B 382, 305, (1992)
[19] Nilles, HP, Dynamically broken supergravity and the hierarchy problem, Phys. Lett., B 115, 193, (1982)
[20] Ferrara, S.; Girardello, L.; Nilles, HP, Breakdown of local supersymmetry through gauge fermion condensates, Phys. Lett., B 125, 457, (1983)
[21] Dine, M.; Rohm, R.; Seiberg, N.; Witten, E., Gluino condensation in superstring models, Phys. Lett., B 156, 55, (1985)
[22] Krasnikov, NV, On supersymmetry breaking in superstring theories, Phys. Lett., B 193, 37, (1987)
[23] Casas, JA; Lalak, Z.; Muñoz, C.; Ross, GG, Hierarchical supersymmetry breaking and dynamical determination of compactification parameters by nonperturbative effects, Nucl. Phys., B 347, 243, (1990)
[24] Carlos, B.; Casas, JA; Muñoz, C., Massive hidden matter and gaugino condensation, Phys. Lett., B 263, 248, (1991)
[25] Carlos, B.; Casas, JA; Muñoz, C., Supersymmetry breaking and determination of the unification gauge coupling constant in string theories, Nucl. Phys., B 399, 623, (1993)
[26] Kachru, S.; Kallosh, R.; Linde, AD; Trivedi, SP, De Sitter vacua in string theory, Phys. Rev., D 68, 046005, (2003)
[27] Kappl, R.; etal., Large hierarchies from approximate R symmetries, Phys. Rev. Lett., 102, 121602, (2009)
[28] B. Dundee, S. Raby and A. Westphal, Moduli stabilization and SUSY breaking in heterotic orbifold string models, arXiv:1002.1081 [SPIRES].
[29] Kaplunovsky, V.; Louis, J., On gauge couplings in string theory, Nucl. Phys., B 444, 191, (1995)
[30] Font, A.; Ibáñez, LE; Lüst, D.; Quevedo, F., Supersymmetry breaking from duality invariant gaugino condensation, Phys. Lett., B 245, 401, (1990)
[31] Cvetič, M.; Font, A.; Ibáñez, LE; Lüst, D.; Quevedo, F., Target space duality, supersymmetry breaking and the stability of classical string vacua, Nucl. Phys., B 361, 194, (1991)
[32] Bailin, D.; Love, A.; Sabra, WA; Thomas, S., Anisotropic solutions for orbifold moduli from duality invariant gaugino condensates, Mod. Phys. Lett., A 9, 2543, (1994)
[33] Lüst, D.; Muñoz, C., Duality invariant gaugino condensation and one loop corrected Kähler potentials in string theory, Phys. Lett., B 279, 272, (1992)
[34] Spalinski, M., On the discrete symmetry group of Narian orbifolds, Phys. Lett., B 275, 47, (1992)
[35] Erler, J.; Jungnickel, D.; Nilles, HP, Space duality and quantized Wilson lines, Phys. Lett., B 276, 303, (1992)
[36] Bailin, D.; Love, A.; Sabra, WA; Thomas, S., Modular symmetries in \(Z\)(\(N\)) orbifold compactified string theories with Wilson lines, Mod. Phys. Lett., A 9, 1229, (1994)
[37] Love, A.; Todd, S., Modular symmetries of threshold corrections for abelian orbifolds with discrete Wilson lines, Nucl. Phys., B 481, 253, (1996)
[38] Senda, I.; Sugamoto, A., Orbifold models and modular transformation, Nucl. Phys., B 302, 291, (1988)
[39] Dixon, LJ; Harvey, JA; Vafa, C.; Witten, E., Strings on orbifolds. 2, Nucl. Phys., B 274, 285, (1986)
[40] Vafa, C., Modular invariance and discrete torsion on orbifolds, Nucl. Phys., B 273, 592, (1986)
[41] Plöger, F.; Ramos-Sánchez, S.; Ratz, M.; Vaudrevange, PKS, Mirage torsion, JHEP, 04, 063, (2007)
[42] Ibáñez, LE; Nilles, HP; Quevedo, F., Reducing the rank of the gauge group in orbifold compactifications of the heterotic string, Phys. Lett., B 192, 332, (1987)
[43] Förste, S.; Nilles, HP; Wingerter, A., Geometry of rank reduction, Phys. Rev., D 72, 026001, (2005)
[44] Kobayashi, T.; Raby, S.; Zhang, R-J, Searching for realistic 4d string models with a Pati-Salam symmetry: orbifold grand unified theories from heterotic string compactification on a Z(6) orbifold, Nucl. Phys., B 704, 3, (2005)
[45] Förste, S.; Nilles, HP; Vaudrevange, PKS; Wingerter, A., Heterotic brane world, Phys. Rev., D 70, 106008, (2004)
[46] Font, A.; Ibáñez, LE; Nilles, HP; Quevedo, F., On the concept of naturalness in string theories, Phys. Lett., B 213, 274, (1988)
[47] Font, A.; Ibáñez, LE; Nilles, HP; Quevedo, F., Yukawa couplings in degenerate orbifolds: towards a realistic SU(3) × SU(2) × U(1) superstring, Phys. Lett., 210B, 101, (1988)
[48] Font, A.; Ibáñez, LE; Quevedo, F.; Sierra, A., The construction of ’realistic’ four-dimensional strings through orbifolds, Nucl. Phys., B 331, 421, (1990)
[49] Dine, M.; Seiberg, N., Couplings and scales in superstring models, Phys. Rev. Lett., 55, 366, (1985)
[50] Ibáñez, LE; Nilles, HP, Low-energy remnants of superstring anomaly cancellation terms, Phys. Lett., B 169, 354, (1986)
[51] Ferrara, S.; Lüst, D.; Theisen, S., Target space modular invariance and low-energy couplings in orbifold compactifications, Phys. Lett., B 233, 147, (1989)
[52] Derendinger, JP; Ferrara, S.; Kounnas, C.; Zwirner, F., On loop corrections to string effective field theories: field dependent gauge couplings and σ-model anomalies, Nucl. Phys., B 372, 145, (1992)
[53] Burwick, TT; Kaiser, RK; Muller, HF, General Yukawa couplings of strings on \(Z\)(\(N\)) orbifolds, Nucl. Phys., B 355, 689, (1991)
[54] Erler, J.; Jungnickel, D.; Spalinski, M.; Stieberger, S., Higher twisted sector couplings of \(Z\)(\(N\)) orbifolds, Nucl. Phys., B 397, 379, (1993)
[55] Casas, JA; Gómez, F.; Muñoz, C., Complete structure of \(Z\)(\(n\)) Yukawa couplings, Int. J. Mod. Phys., A 8, 455, (1993)
[56] J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton Univ. Press, Princeton U.S.A. (1992) [SPIRES].
[57] Choi, K-S; Kobayashi, T., Higher order couplings from heterotic orbifold theory, Nucl. Phys., B 797, 295, (2008)
[58] Kiritsis, E.; Kounnas, C.; Petropoulos, PM; Rizos, J., Universality properties of N = 2 and N = 1 heterotic threshold corrections, Nucl. Phys., B 483, 141, (1997)
[59] Nilles, HP; Stieberger, S., String unification, universal one-loop corrections and strongly coupled heterotic string theory, Nucl. Phys., B 499, 3, (1997)
[60] Bailin, D.; Kraniotis, GV; Love, A., CP violation including universal one-loop corrections and heterotic M-theory, Phys. Lett., B 483, 425, (2000)
[61] Dixon, LJ; Kaplunovsky, V.; Louis, J., Moduli dependence of string loop corrections to gauge coupling constants, Nucl. Phys., B 355, 649, (1991)
[62] J. Louis, Nonharmonic gauge coupling constants in supersymmetry and superstring theory, proceedings of 2nd International Symposium on Particles, Strings and Cosmology, Boston U.S.A. (1991) [SPIRES].
[63] Casas, JA; Katehou, EK; Muñoz, C., U(1) charges in orbifolds: anomaly cancellation and phenomenological consequences, Nucl. Phys., B 317, 171, (1989)
[64] Kobayashi, T.; Nakano, H., *anomalous* U(1) symmetry in orbifold string models, Nucl. Phys., B 496, 103, (1997)
[65] Buccella, F.; Derendinger, JP; Ferrara, S.; Savoy, CA, Patterns of symmetry breaking in supersymmetric gauge theories, Phys. Lett., B 115, 375, (1982)
[66] Dudas, E.; Mambrini, Y.; Pokorski, S.; Romagnoni, A., Moduli stabilization with Fayet-Iliopoulos uplift, JHEP, 04, 015, (2008)
[67] Gallego, D.; Serone, M., Moduli stabilization in non-supersymmetric Minkowski vacua with anomalous U(1) symmetry, JHEP, 08, 025, (2008)
[68] Lebedev, O.; Nilles, HP; Ratz, M., De Sitter vacua from matter superpotentials, Phys. Lett., B 636, 126, (2006)
[69] Lebedev, O.; Lowen, V.; Mambrini, Y.; Nilles, HP; Ratz, M., Metastable vacua in flux compactifications and their phenomenology, JHEP, 02, 063, (2007)
[70] Löwen, V.; Nilles, HP, Mirage pattern from the heterotic string, Phys. Rev., D 77, 106007, (2008)
[71] Y. Akrami et al., work in progress.
[72] Ramos-Sánchez, S., Towards low energy physics from the heterotic string, Fortsch. Phys., 10, 907, (2009)
[73] M.A. Klaput and C. Paleani, The computation of one-loop heterotic string threshold corrections for general orbifold models with discrete Wilson lines, arXiv:1001. 1480 [SPIRES].
[74] Cvetič, M.; Everett, LL; Wang, J., Units and numerical values of the effective couplings in perturbative heterotic string vacua, Phys. Rev., D 59, 107901, (1999)
[75] S.L. Parameswaran, S. Ramos-Sánchez and I. Zavala, http://www.th.physik.uni-bonn.de/nilles/Z6IIorbifold/moduli/.
[76] Gersdorff, G.; Hebecker, A., Radius stabilization by two-loop Casimir energy, Nucl. Phys., B 720, 211, (2005)
[77] Gross, C.; Hebecker, A., A realistic unified gauge coupling from the micro-landscape of orbifold guts, Nucl. Phys., B 821, 354, (2009)
[78] Buchmüller, W.; Catena, R.; Schmidt-Hoberg, K., Enhanced symmetries of orbifolds from moduli stabilization, Nucl. Phys., B 821, 1, (2009)
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