Abstract
We investigate de Sitter solutions of \( \mathcal{N}=1 \) supergravity with an F-term scalar potential near a no-scale Minkowski point, as they may in particular arise from flux compactifications in string theory. We show that a large class of such solutions has a universal tachyon with \( \eta \le -\frac{4}{3} \) at positive vacuum energies, thus forbidding meta-stable de Sitter vacua and slow-roll inflation. The tachyon aligns with the sgoldstino in the Minkowski limit, whereas the sgoldstino itself is generically stable in the de Sitter vacuum due to mass mixing effects. We specify necessary conditions for the superpotential and the Kähler potential to avoid the instability. Our result may also help to explain why the program of classical de Sitter hunting has remained unsuccessful, while constructions involving instantons or non-geometric fluxes have led to various examples of meta-stable de Sitter vacua.
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].
C.P. Burgess, R. Kallosh and F. Quevedo, De Sitter string vacua from supersymmetric D terms, JHEP 10 (2003) 056 [hep-th/0309187] [INSPIRE].
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [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].
J. Louis, M. Rummel, R. Valandro and A. Westphal, Building an explicit de Sitter, JHEP 10 (2012) 163 [arXiv:1208.3208] [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, D. Klevers, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, Explicit de Sitter flux vacua for global string models with chiral matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].
J. Blåbäck, D. Roest and I. Zavala, De Sitter vacua from nonperturbative 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. Rummel and Y. Sumitomo, De Sitter vacua from a D-term generated racetrack uplift, JHEP 01 (2015) 015 [arXiv:1407.7580] [INSPIRE].
A.P. Braun, M. Rummel, Y. Sumitomo and R. Valandro, De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications, JHEP 12 (2015) 033 [arXiv:1509.06918] [INSPIRE].
R. Kallosh, A. Linde, B. Vercnocke and T. Wrase, Analytic classes of metastable de Sitter vacua, JHEP 10 (2014) 011 [arXiv:1406.4866] [INSPIRE].
M.C.D. Marsh, B. Vercnocke and T. Wrase, Decoupling and de Sitter vacua in approximate no-scale supergravities, JHEP 05 (2015) 081 [arXiv:1411.6625] [INSPIRE].
A. Guarino and G. Inverso, Single-step de Sitter vacua from nonperturbative effects with matter, Phys. Rev. D 93 (2016) 066013 [arXiv:1511.07841] [INSPIRE].
A. Retolaza and A. Uranga, De Sitter uplift with dynamical SUSY breaking, JHEP 04 (2016) 137 [arXiv:1512.06363] [INSPIRE].
X. Dong, B. Horn, E. Silverstein and G. Torroba, Micromanaging de Sitter holography, Class. Quant. Grav. 27 (2010) 245020 [arXiv:1005.5403] [INSPIRE].
M. Dodelson, X. Dong, E. Silverstein and G. Torroba, New solutions with accelerated expansion in string theory, JHEP 12 (2014) 050 [arXiv:1310.5297] [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].
G. Dibitetto, R. Linares and D. Roest, Flux compactifications, gauge algebras and de Sitter, Phys. Lett. B 688 (2010) 96 [arXiv:1001.3982] [INSPIRE].
U. Danielsson and G. Dibitetto, On the distribution of stable de Sitter vacua, JHEP 03 (2013) 018 [arXiv:1212.4984] [INSPIRE].
J. Blåbäck, U. Danielsson and G. Dibitetto, Fully stable dS vacua from generalised fluxes, JHEP 08 (2013) 054 [arXiv:1301.7073] [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].
F. Hassler, D. Lüst and S. Massai, On inflation and de Sitter in non-geometric string backgrounds, Fortsch. Phys. 65 (2017) 1700062 [arXiv:1405.2325] [INSPIRE].
J. Blåbäck, U.H. Danielsson, G. Dibitetto and S.C. Vargas, Universal dS vacua in STU-models, JHEP 10 (2015) 069 [arXiv:1505.04283] [INSPIRE].
M. Cicoli, S. de Alwis and A. Westphal, Heterotic moduli stabilisation, JHEP 10 (2013) 199 [arXiv:1304.1809] [INSPIRE].
S.L. Parameswaran and A. Westphal, De Sitter string vacua from perturbative Kähler corrections and consistent D-terms, JHEP 10 (2006) 079 [hep-th/0602253] [INSPIRE].
C. Kounnas, D. Lüst and N. Toumbas, R 2 inflation from scale invariant supergravity and anomaly free superstrings with fluxes, Fortsch. Phys. 63 (2015) 12 [arXiv:1409.7076] [INSPIRE].
A. Achúcarro, P. Ortiz and K. Sousa, A new class of de Sitter vacua in string theory compactifications, Phys. Rev. D 94 (2016) 086012 [arXiv:1510.01273] [INSPIRE].
M. Cicoli, F. Quevedo and R. Valandro, De Sitter from T-branes, JHEP 03 (2016) 141 [arXiv:1512.04558] [INSPIRE].
I. Ben-Dayan, S. Jing, A. Westphal and C. Wieck, Accidental inflation from Kähler uplifting, JCAP 03 (2014) 054 [arXiv:1309.0529] [INSPIRE].
R. Blumenhagen et al., A flux-scaling scenario for high-scale moduli stabilization in string theory, Nucl. Phys. B 897 (2015) 500 [arXiv:1503.07634] [INSPIRE].
R. Blumenhagen, C. Damian, A. Font, D. Herschmann and R. Sun, The flux-scaling scenario: de Sitter uplift and axion inflation, Fortsch. Phys. 64 (2016) 536 [arXiv:1510.01522] [INSPIRE].
Y. Sumitomo and S.-H. Henry Tye, A stringy mechanism for a small cosmological constant, JCAP 08 (2012) 032 [arXiv:1204.5177] [INSPIRE].
Y. Sumitomo and S.-H. Henry Tye, A stringy mechanism for a small cosmological constant — multi-moduli cases, JCAP 02 (2013) 006 [arXiv:1209.5086] [INSPIRE].
S.-H. Henry Tye and S.S.C. Wong, Linking light scalar modes with a small positive cosmological constant in string theory, JHEP 06 (2017) 094 [arXiv:1611.05786] [INSPIRE].
G.W. Gibbons, Aspects of supergravity theories, in Supersymmetry, supergravity and related topics, F. del Aguila, J.A. de Azcárraga and L.E. Ibáñez eds., World Scientific, (1985), pg. 346 [INSPIRE].
B. de Wit, D.J. Smit and N.D. Hari Dass, Residual supersymmetry of compactified D = 10 supergravity, Nucl. Phys. B 283 (1987) 165 [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary constraints on type IIA string theory, JHEP 12 (2007) 095 [arXiv:0711.2512] [INSPIRE].
E. Silverstein, Simple de Sitter solutions, Phys. Rev. D 77 (2008) 106006 [arXiv:0712.1196] [INSPIRE].
S.S. Haque, G. Shiu, B. Underwood and T. Van Riet, Minimal simple de Sitter solutions, Phys. Rev. D 79 (2009) 086005 [arXiv:0810.5328] [INSPIRE].
P.J. Steinhardt and D. Wesley, Dark energy, inflation and extra dimensions, Phys. Rev. D 79 (2009) 104026 [arXiv:0811.1614] [INSPIRE].
C. Caviezel, P. Koerber, S. Körs, D. Lüst, T. Wrase and M. Zagermann, On the cosmology of type IIA compactifications on SU(3)-structure manifolds, JHEP 04 (2009) 010 [arXiv:0812.3551] [INSPIRE].
R. Flauger, S. Paban, D. Robbins and T. Wrase, Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes, Phys. Rev. D 79 (2009) 086011 [arXiv:0812.3886] [INSPIRE].
U.H. Danielsson, S.S. Haque, G. Shiu and T. Van Riet, Towards classical de Sitter solutions in string theory, JHEP 09 (2009) 114 [arXiv:0907.2041] [INSPIRE].
C. Caviezel, T. Wrase and M. Zagermann, Moduli stabilization and cosmology of type IIB on SU(2)-structure orientifolds, JHEP 04 (2010) 011 [arXiv:0912.3287] [INSPIRE].
T. Wrase and M. Zagermann, On classical de Sitter vacua in string theory, Fortsch. Phys. 58 (2010) 906 [arXiv:1003.0029] [INSPIRE].
T. Van Riet, On classical de Sitter solutions in higher dimensions, Class. Quant. Grav. 29 (2012) 055001 [arXiv:1111.3154] [INSPIRE].
D. Andriot and J. Blåbäck, Refining the boundaries of the classical de Sitter landscape, JHEP 03 (2017) 102 [Erratum ibid. 03 (2018) 083] [arXiv:1609.00385] [INSPIRE].
S.R. Green, E.J. Martinec, C. Quigley and S. Sethi, Constraints on string cosmology, Class. Quant. Grav. 29 (2012) 075006 [arXiv:1110.0545] [INSPIRE].
F.F. Gautason, D. Junghans and M. Zagermann, On cosmological constants from α′-corrections, JHEP 06 (2012) 029 [arXiv:1204.0807] [INSPIRE].
D. Kutasov, T. Maxfield, I. Melnikov and S. Sethi, Constraining de Sitter space in string theory, Phys. Rev. Lett. 115 (2015) 071305 [arXiv:1504.00056] [INSPIRE].
C. Quigley, Gaugino condensation and the cosmological constant, JHEP 06 (2015) 104 [arXiv:1504.00652] [INSPIRE].
F. Denef and M.R. Douglas, Distributions of nonsupersymmetric flux vacua, JHEP 03 (2005) 061 [hep-th/0411183] [INSPIRE].
D. Marsh, L. McAllister and T. Wrase, The wasteland of random supergravities, JHEP 03 (2012) 102 [arXiv:1112.3034] [INSPIRE].
X. Chen, G. Shiu, Y. Sumitomo and S.-H. Henry Tye, A global view on the search for de Sitter vacua in (type IIA) string theory, JHEP 04 (2012) 026 [arXiv:1112.3338] [INSPIRE].
T.C. Bachlechner, D. Marsh, L. McAllister and T. Wrase, Supersymmetric vacua in random supergravity, JHEP 01 (2013) 136 [arXiv:1207.2763] [INSPIRE].
U.H. Danielsson, P. Koerber and T. Van Riet, Universal de Sitter solutions at tree-level, JHEP 05 (2010) 090 [arXiv:1003.3590] [INSPIRE].
U.H. Danielsson, S.S. Haque, P. Koerber, G. Shiu, T. Van Riet and T. Wrase, De Sitter hunting in a classical landscape, Fortsch. Phys. 59 (2011) 897 [arXiv:1103.4858] [INSPIRE].
G. Shiu and Y. Sumitomo, Stability constraints on classical de Sitter vacua, JHEP 09 (2011) 052 [arXiv:1107.2925] [INSPIRE].
U.H. Danielsson, G. Shiu, T. Van Riet and T. Wrase, A note on obstinate tachyons in classical dS solutions, JHEP 03 (2013) 138 [arXiv:1212.5178] [INSPIRE].
L. Covi, M. Gómez-Reino, C. Gross, J. Louis, G.A. Palma and C.A. Scrucca, 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, J. Louis, G.A. Palma and C.A. Scrucca, Constraints on modular inflation in supergravity and string theory, JHEP 08 (2008) 055 [arXiv:0805.3290] [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].
M. Gomez-Reino and C.A. Scrucca, Locally stable non-supersymmetric Minkowski vacua in supergravity, JHEP 05 (2006) 015 [hep-th/0602246] [INSPIRE].
M. Gomez-Reino and C.A. Scrucca, Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity, JHEP 09 (2006) 008 [hep-th/0606273] [INSPIRE].
M. Gomez-Reino and C.A. Scrucca, Metastable supergravity vacua with F and D supersymmetry breaking, JHEP 08 (2007) 091 [arXiv:0706.2785] [INSPIRE].
I. Ben-Dayan, R. Brustein and S.P. de Alwis, Models of modular inflation and their phenomenological consequences, JCAP 07 (2008) 011 [arXiv:0802.3160] [INSPIRE].
M. Badziak and M. Olechowski, Volume modulus inflation and a low scale of SUSY breaking, JCAP 07 (2008) 021 [arXiv:0802.1014] [INSPIRE].
A. Hetz and G.A. Palma, Sound speed of primordial fluctuations in supergravity inflation, Phys. Rev. Lett. 117 (2016) 101301 [arXiv:1601.05457] [INSPIRE].
D. Junghans, Tachyons in classical de Sitter vacua, JHEP 06 (2016) 132 [arXiv:1603.08939] [INSPIRE].
E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos, Naturally vanishing cosmological constant in N = 1 supergravity, Phys. Lett. B 133 (1983) 61 [INSPIRE].
J.R. Ellis, A.B. Lahanas, D.V. Nanopoulos and K. Tamvakis, No-scale supersymmetric Standard Model, Phys. Lett. B 134 (1984) 429 [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].
P.G. Camara and M. Graña, No-scale supersymmetry breaking vacua and soft terms with torsion, JHEP 02 (2008) 017 [arXiv:0710.4577] [INSPIRE].
E. Palti, G. Tasinato and J. Ward, Weakly-coupled IIA flux compactifications, JHEP 06 (2008) 084 [arXiv:0804.1248] [INSPIRE].
J. Blåbäck, U.H. Danielsson, D. Junghans, T. Van Riet, T. Wrase and M. Zagermann, Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [INSPIRE].
D. Andriot, J. Blåbäck and T. Van Riet, Minkowski flux vacua of type-II supergravities, Phys. Rev. Lett. 118 (2017) 011603 [Erratum ibid. 120 (2018) 169901] [arXiv:1609.00729] [INSPIRE].
K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and α′ corrections to flux induced potentials, JHEP 06 (2002) 060 [hep-th/0204254] [INSPIRE].
F. Bonetti and M. Weissenbacher, The Euler characteristic correction to the Kähler potential — revisited, JHEP 01 (2017) 003 [arXiv:1608.01300] [INSPIRE].
M. Berg, M. Haack and E. Pajer, Jumping through loops: on soft terms from large volume compactifications, JHEP 09 (2007) 031 [arXiv:0704.0737] [INSPIRE].
M. Cicoli, J.P. Conlon and F. Quevedo, Systematics of string loop corrections in type IIB Calabi-Yau flux compactifications, JHEP 01 (2008) 052 [arXiv:0708.1873] [INSPIRE].
T. House and E. Palti, Effective action of (massive) IIA on manifolds with SU(3) structure, Phys. Rev. D 72 (2005) 026004 [hep-th/0505177] [INSPIRE].
M. Graña, J. Louis and D. Waldram, Hitchin functionals in N = 2 supergravity, JHEP 01 (2006) 008 [hep-th/0505264] [INSPIRE].
M. Graña, J. Louis and D. Waldram, SU(3) × SU(3) compactification and mirror duals of magnetic fluxes, JHEP 04 (2007) 101 [hep-th/0612237] [INSPIRE].
I. Benmachiche and T.W. Grimm, Generalized N = 1 orientifold compactifications and the Hitchin functionals, Nucl. Phys. B 748 (2006) 200 [hep-th/0602241] [INSPIRE].
P. Koerber and L. Martucci, From ten to four and back again: how to generalize the geometry, JHEP 08 (2007) 059 [arXiv:0707.1038] [INSPIRE].
O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].
G. Villadoro and F. Zwirner, Beyond twisted tori, Phys. Lett. B 652 (2007) 118 [arXiv:0706.3049] [INSPIRE].
R. Kallosh and T. Wrase, Emergence of spontaneously broken supersymmetry on an anti-D3-brane in KKLT dS vacua, JHEP 12 (2014) 117 [arXiv:1411.1121] [INSPIRE].
E.A. Bergshoeff, K. Dasgupta, R. Kallosh, A. Van Proeyen and T. Wrase, \( \overline{\mathrm{D}3} \) and dS, JHEP 05 (2015) 058 [arXiv:1502.07627] [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: 1612.06847
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Junghans, D., Zagermann, M. A universal tachyon in nearly no-scale de Sitter compactifications. J. High Energ. Phys. 2018, 78 (2018). https://doi.org/10.1007/JHEP07(2018)078
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2018)078