Abstract
In this paper, we give a systematic procedure for building locally stable dS vacua in \( \mathcal{N}=1 \) supergravity models motivated by string theory. We assume that one of the superfields has a Kähler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order ϵ. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by ϵ and the cosmological constant. These regions exist regardless of the details of the other moduli, provided the superpotential can be tuned such that the off-diagonal blocks of the mass matrix are parametrically small. We test and support this general dS landscape construction by explicit analytic solutions for the STU model. The Minkowski limits of these dS vacua either break supersymmetry or have flat directions in agreement with a no-go theorem that we prove, stating that a supersymmetric Minkowski vacuum without flat directions cannot be continuously deformed into a non-supersymmetric vacuum. We also describe a method for finding a broad class of stable supersymmetric Minkowski vacua that can be F-term uplifted to dS vacua and which have an easily controllable SUSY breaking scale.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
SDSS collaboration, M. Betoule et al., Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples, Astron. Astrophys. (2014) [arXiv:1401.4064] [INSPIRE].
A. Saltman and E. Silverstein, The Scaling of the no scale potential and de Sitter model building, JHEP 11 (2004) 066 [hep-th/0402135] [INSPIRE].
L. Covi et al., de Sitter vacua in no-scale supergravities and Calabi-Yau string models, JHEP 06 (2008) 057 [arXiv:0804.1073] [INSPIRE].
L. Covi, M. Gomez-Reino, C. Gross, G.A. Palma and C.A. Scrucca, Constructing de Sitter vacua in no-scale string models without uplifting, JHEP 03 (2009) 146 [arXiv:0812.3864] [INSPIRE].
J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].
B. de Carlos, A. Guarino and J.M. Moreno, Flux moduli stabilisation, Supergravity algebras and no-go theorems, JHEP 01 (2010) 012 [arXiv:0907.5580] [INSPIRE].
B. de Carlos, A. Guarino and J.M. Moreno, Complete classification of Minkowski vacua in generalised flux models, JHEP 02 (2010) 076 [arXiv:0911.2876] [INSPIRE].
U. Danielsson and G. Dibitetto, On the distribution of stable de Sitter vacua, JHEP 03 (2013) 018 [arXiv:1212.4984] [INSPIRE].
J. Blabäck, U. Danielsson and G. Dibitetto, Fully stable dS vacua from generalised fluxes, JHEP 08 (2013) 054 [arXiv:1301.7073] [INSPIRE].
O. Lebedev, H.P. Nilles and M. Ratz, de Sitter vacua from matter superpotentials, Phys. Lett. B 636 (2006) 126 [hep-th/0603047] [INSPIRE].
A. Westphal, de Sitter string vacua from Kähler uplifting, JHEP 03 (2007) 102 [hep-th/0611332] [INSPIRE].
M. Rummel and A. Westphal, A sufficient condition for de Sitter vacua in type IIB string theory, JHEP 01 (2012) 020 [arXiv:1107.2115] [INSPIRE].
M. Cicoli, A. Maharana, F. Quevedo and C.P. Burgess, de Sitter String Vacua from Dilaton-dependent Non-perturbative Effects, JHEP 06 (2012) 011 [arXiv:1203.1750] [INSPIRE].
M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, D-Branes at del Pezzo Singularities: Global Embedding and Moduli Stabilisation, JHEP 09 (2012) 019 [arXiv:1206.5237] [INSPIRE].
A. Hebecker, S.C. Kraus, M. Kuntzler, D. Lüst and T. Weigand, Fluxbranes: Moduli Stabilisation and Inflation, JHEP 01 (2013) 095 [arXiv:1207.2766] [INSPIRE].
J. Louis, M. Rummel, R. Valandro and A. Westphal, Building an explicit de Sitter, JHEP 10 (2012) 163 [arXiv:1208.3208] [INSPIRE].
C. Damian, L.R. Diaz-Barron, O. Loaiza-Brito and M. Sabido, Slow-Roll Inflation in Non-geometric Flux Compactification, JHEP 06 (2013) 109 [arXiv:1302.0529] [INSPIRE].
C. Damian and O. Loaiza-Brito, More stable de Sitter vacua from S-dual nongeometric fluxes, Phys. Rev. D 88 (2013) 046008 [arXiv:1304.0792] [INSPIRE].
M. Cicoli et al., Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].
J. Blabäck, D. Roest and I. Zavala, de Sitter Vacua from Non-perturbative Flux Compactifications, Phys. Rev. D 90 (2014) 024065 [arXiv:1312.5328] [INSPIRE].
U. Danielsson and G. Dibitetto, An alternative to anti-branes and O-planes?, JHEP 05 (2014) 013 [arXiv:1312.5331] [INSPIRE].
M. Dine and N. Seiberg, Is the Superstring Weakly Coupled?, Phys. Lett. B 162 (1985) 299 [INSPIRE].
R. Kallosh and A.D. Linde, Landscape, the scale of SUSY breaking and inflation, JHEP 12 (2004) 004 [hep-th/0411011] [INSPIRE].
J.J. Blanco-Pillado, R. Kallosh and A.D. Linde, Supersymmetry and stability of flux vacua, JHEP 05 (2006) 053 [hep-th/0511042] [INSPIRE].
D. Marsh, L. McAllister and T. Wrase, The Wasteland of Random Supergravities, JHEP 03 (2012) 102 [arXiv:1112.3034] [INSPIRE].
M. Dine, R. Kitano, A. Morisse and Y. Shirman, Moduli decays and gravitinos, Phys. Rev. D 73 (2006) 123518 [hep-ph/0604140] [INSPIRE].
R. Kallosh and A.D. Linde, O’KKLT, JHEP 02 (2007) 002 [hep-th/0611183] [INSPIRE].
E. Dudas, A. Linde, Y. Mambrini, A. Mustafayev and K.A. Olive, Strong moduli stabilization and phenomenology, Eur. Phys. J. C 73 (2013) 2268 [arXiv:1209.0499] [INSPIRE].
F. Denef and M.R. Douglas, Distributions of nonsupersymmetric flux vacua, JHEP 03 (2005) 061 [hep-th/0411183] [INSPIRE].
R. Brustein and S.P. de Alwis, Moduli potentials in string compactifications with fluxes: Mapping the discretuum, Phys. Rev. D 69 (2004) 126006 [hep-th/0402088] [INSPIRE].
R. Kallosh and S. Prokushkin, SuperCosmology, hep-th/0403060 [INSPIRE].
M. Berg, M. Haack and B. Körs, Loop corrections to volume moduli and inflation in string theory, Phys. Rev. D 71 (2005) 026005 [hep-th/0404087] [INSPIRE].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
R. Kallosh and A.D. Linde, Testing String Theory with CMB, JCAP 04 (2007) 017 [arXiv:0704.0647] [INSPIRE].
A. Achucarro, B. de Carlos, J.A. Casas and L. Doplicher, de Sitter vacua from uplifting D-terms in effective supergravities from realistic strings, JHEP 06 (2006) 014 [hep-th/0601190] [INSPIRE].
E. Dudas, C. Papineau and S. Pokorski, Moduli stabilization and uplifting with dynamically generated F-terms, JHEP 02 (2007) 028 [hep-th/0610297] [INSPIRE].
H. Abe, T. Higaki, T. Kobayashi and Y. Omura, Moduli stabilization, F-term uplifting and soft supersymmetry breaking terms, Phys. Rev. D 75 (2007) 025019 [hep-th/0611024] [INSPIRE].
S.L. Parameswaran and A. Westphal, Consistent de Sitter string vacua from Kähler stabilization and D-term uplifting, Fortsch. Phys. 55 (2007) 804 [hep-th/0701215] [INSPIRE].
J.L. Evans, M.A.G. Garcia and K.A. Olive, The Moduli and Gravitino (non)-Problems in Models with Strongly Stabilized Moduli, JCAP 03 (2014) 022 [arXiv:1311.0052] [INSPIRE].
U.H. Danielsson et al., de Sitter hunting in a classical landscape, Fortsch. Phys. 59 (2011) 897 [arXiv:1103.4858] [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: 1406.4866
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
Kallosh, R., Linde, A., Vercnocke, B. et al. Analytic classes of metastable de Sitter vacua. J. High Energ. Phys. 2014, 11 (2014). https://doi.org/10.1007/JHEP10(2014)011
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2014)011