Abstract
We derive highly constraining no-go theorems for classical de Sitter backgrounds of string theory, with parallel sources; this should impact the embedding of cosmological models. We study ten-dimensional vacua of type II supergravities with parallel and backreacted orientifold O p -planes and D p -branes, on four-dimensional de Sitter spacetime times a compact manifold. Vacua for p = 3, 7 or 8 are completely excluded, and we obtain tight constraints for p = 4, 5, 6. This is achieved through the derivation of an enlightening expression for the four-dimensional Ricci scalar. Further interesting expressions and no-go theorems are obtained. The paper is self-contained so technical aspects, including conventions, might be of more general interest.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
13 March 2018
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP03(2018)083
References
BICEP2, Planck collaboration, P.A.R. Ade et al., Joint Analysis of BICEP2/KeckArray and Planck data, Phys. Rev. Lett. 114 (2015) 101301 [arXiv:1502.00612] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XVII. Constraints on primordial non-Gaussianity, Astron. Astrophys. 594 (2016) A17 [arXiv:1502.01592] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
X. Chen, C. Dvorkin, Z. Huang, M.H. Namjoo and L. Verde, The future of primordial features with large-scale structure surveys, JCAP 11 (2016) 014 [arXiv:1605.09365] [INSPIRE].
S.L. Parameswaran and I. Zavala, Prospects for primordial gravitational waves in string inflation, Int. J. Mod. Phys. D 25 (2016) 1644011 [arXiv:1606.02537] [INSPIRE].
J.P. Conlon, The QCD axion and moduli stabilisation, JHEP 05 (2006) 078 [hep-th/0602233] [INSPIRE].
D. Andriot, A no-go theorem for monodromy inflation, JCAP 03 (2016) 025 [arXiv:1510.02005] [INSPIRE].
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].
I. Bena, M. Graña and N. Halmagyi, On the existence of meta-stable vacua in Klebanov-Strassler, JHEP 09 (2010) 087 [arXiv:0912.3519] [INSPIRE].
I. Bena, J. Blabäck and D. Turton, Loop corrections to the antibrane potential, JHEP 07 (2016) 132 [arXiv:1602.05959] [INSPIRE].
S.P. de Alwis, Constraints on Dbar uplifts, JHEP 11 (2016) 045 [arXiv:1605.06456] [INSPIRE].
N. Cabo Bizet and S. Hirano, Revisiting constraints on uplifts to de Sitter vacua, arXiv:1607.01139 [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].
G.W. Gibbons, Aspects of supergravity theories, XV GIFT Seminar on Supersymmetry and Supergravity, June 4–11, Gerona, Spain (1984).
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].
P.K. Townsend, Cosmic acceleration and M-theory, hep-th/0308149 [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].
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].
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].
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].
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].
C.P. Burgess, A. Maharana, L. van Nierop, A.A. Nizami and F. Quevedo, On brane back-reaction and de Sitter solutions in higher-dimensional supergravity, JHEP 04 (2012) 018 [arXiv:1109.0532] [INSPIRE].
T. Van Riet, On classical de Sitter solutions in higher dimensions, Class. Quant. Grav. 29 (2012) 055001 [arXiv:1111.3154] [INSPIRE].
F.F. Gautason, D. Junghans and M. Zagermann, Cosmological constant, near brane behavior and singularities, JHEP 09 (2013) 123 [arXiv:1301.5647] [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].
E. Silverstein, Simple de Sitter solutions, Phys. Rev. D 77 (2008) 106006 [arXiv:0712.1196] [INSPIRE].
J. Blaback, 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. Junghans, Backreaction of localised sources in string compactifications, arXiv:1309.5990 [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].
L. Covi, M. Gomez-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].
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].
D. Junghans, Tachyons in classical de Sitter vacua, JHEP 06 (2016) 132 [arXiv:1603.08939] [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].
D. Andriot, J. Blabäck and T. Van Riet, Minkowski flux vacua of type-II supergravities, Phys. Rev. Lett. 118 (2017) 011603 [arXiv:1609.00729] [INSPIRE].
D. Andriot, E. Goi, R. Minasian and M. Petrini, Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory, JHEP 05 (2011) 028 [arXiv:1003.3774] [INSPIRE].
D. Andriot, New supersymmetric vacua on solvmanifolds, JHEP 02 (2016) 112 [arXiv:1507.00014] [INSPIRE].
L. Martucci and P. Smyth, Supersymmetric D-branes and calibrations on general N = 1 backgrounds, JHEP 11 (2005) 048 [hep-th/0507099] [INSPIRE].
G. Villadoro and F. Zwirner, On general flux backgrounds with localized sources, JHEP 11 (2007) 082 [arXiv:0710.2551] [INSPIRE].
J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].
E. Silverstein and A. Westphal, Monodromy in the CMB: gravity waves and string inflation, Phys. Rev. D 78 (2008) 106003 [arXiv:0803.3085] [INSPIRE].
P. Koerber and L. Martucci, D-branes on AdS flux compactifications, JHEP 01 (2008) 047 [arXiv:0710.5530] [INSPIRE].
M. Berasaluce-González, G. Honecker and A. Seifert, Towards geometric D6-brane model building on non-factorisable toroidal \( {\mathrm{\mathbb{Z}}}_4 \) -orbifolds, JHEP 08 (2016) 062 [arXiv:1606.04926] [INSPIRE].
D. Andriot, Heterotic string from a higher dimensional perspective, Nucl. Phys. B 855 (2012) 222 [arXiv:1102.1434] [INSPIRE].
E. Bergshoeff, R. Kallosh, T. Ort´in, D. Roest and A. Van Proeyen, New formulations of D = 10 supersymmetry and D8-O8 domain walls, Class. Quant. Grav. 18 (2001) 3359 [hep-th/0103233] [INSPIRE].
P. Koerber and D. Tsimpis, Supersymmetric sources, integrability and generalized-structure compactifications, JHEP 08 (2007) 082 [arXiv:0706.1244] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A scan for new N = 1 vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].
E. Bergshoeff and P.K. Townsend, Super D-branes, Nucl. Phys. B 490 (1997) 145 [hep-th/9611173] [INSPIRE].
D. Lüst, F. Marchesano, L. Martucci and D. Tsimpis, Generalized non-supersymmetric flux vacua, JHEP 11 (2008) 021 [arXiv:0807.4540] [INSPIRE].
P. Koerber, Lectures on generalized complex geometry for physicists, Fortsch. Phys. 59 (2011) 169 [arXiv:1006.1536] [INSPIRE].
P. Koerber, Stable D-branes, calibrations and generalized Calabi-Yau geometry, JHEP 08 (2005) 099 [hep-th/0506154] [INSPIRE].
P. Koerber and L. Martucci, Deformations of calibrated D-branes in flux generalized complex manifolds, JHEP 12 (2006) 062 [hep-th/0610044] [INSPIRE].
F. Gmeiner and F. Witt, Calibrations and T-duality, Commun. Math. Phys. 283 (2008) 543 [math/0605710] [INSPIRE].
L. Martucci, Electrified branes, JHEP 02 (2012) 097 [arXiv:1110.0627] [INSPIRE].
D. Andriot and A. Betz, β-supergravity: a ten-dimensional theory with non-geometric fluxes and its geometric framework, JHEP 12 (2013) 083 [arXiv:1306.4381] [INSPIRE].
D. Andriot and A. Betz, NS-branes, source corrected Bianchi identities and more on backgrounds with non-geometric fluxes, JHEP 07 (2014) 059 [arXiv:1402.5972] [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: 1609.00385
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
Andriot, D., Blåbäck, J. Refining the boundaries of the classical de Sitter landscape. J. High Energ. Phys. 2017, 102 (2017). https://doi.org/10.1007/JHEP03(2017)102
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2017)102