Abstract
We construct a new class of metastable de Sitter vacua of flux compactifications of type IIB string theory. These solutions provide a natural extension of the ‘Large Volume Scenario’ anti-de Sitter vacua, and can analogously be realised at parametrically large volume and weak string coupling, using standard \( \mathcal{N} \) = 1 supergravity. For these new vacua, a positive vacuum energy is achieved from the inclusion of a small amount of flux-induced supersymmetry breaking in the complex structure and axio-dilaton sector, and no additional ‘uplift’ contribution (e.g. from anti-branes) is required. We show that the approximate no-scale structure of the effective theory strongly influences the spectrum of the stabilised moduli: one complex structure modulus remains significantly lighter than the supersymmetry breaking scale, and metastability requires only modest amounts of tuning. After discussing these general results, we provide a recipe for constructing de Sitter vacua on a given compactification manifold, and give an explicit example of a de Sitter vacuum for the compactification on the Calabi-Yau orientifold realised in \( \mathbb{C}{\mathrm{\mathbb{P}}}_{11169}^4 \). Finally, we note that these solutions have intriguing implications for phenomenology, predicting no csuperpartners in the spectrum below ∼50 TeV, and no WIMP dark matter.
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References
M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].
F. Denef, Les Houches lectures on constructing string vacua, in String theory and the real world: from particle physics to astrophysics. Proceedings, Summer School in Theoretical Physics, 87th Session, Les Houches France, 2-27 July 2007, pg. 483 [arXiv:0803.1194] [INSPIRE].
M.R. Douglas, The statistics of string/M theory vacua, JHEP 05 (2003) 046 [hep-th/0303194] [INSPIRE].
S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [INSPIRE].
F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP 05 (2004) 072 [hep-th/0404116] [INSPIRE].
F. Denef and M.R. Douglas, Distributions of nonsupersymmetric flux vacua, JHEP 03 (2005) 061 [hep-th/0411183] [INSPIRE].
M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four-dimensions, Adv. Theor. Math. Phys. 4 (2002) 1209 [hep-th/0002240] [INSPIRE].
M. Lynker, R. Schimmrigk and A. Wisskirchen, Landau-Ginzburg vacua of string, M-theory and F-theory at c = 12, Nucl. Phys. B 550 (1999) 123 [hep-th/9812195] [INSPIRE].
Supernova Search Team collaboration, A.G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009 [astro-ph/9805201] [INSPIRE].
Supernova Cosmology Project collaboration, S. Perlmutter et al., Measurements of Ω and Λ from 42 high redshift supernovae, Astrophys. J. 517 (1999) 565 [astro-ph/9812133] [INSPIRE].
A. Aazami and R. Easther, Cosmology from random multifield potentials, JCAP 03 (2006) 013 [hep-th/0512050] [INSPIRE].
D. Marsh, L. McAllister and T. Wrase, The wasteland of random supergravities, JHEP 03 (2012) 102 [arXiv:1112.3034] [INSPIRE].
T.C. Bachlechner, On Gaussian random supergravity, JHEP 04 (2014) 054 [arXiv:1401.6187] [INSPIRE].
A.J. Bray and D.S. Dean, Statistics of critical points of Gaussian fields on large-dimensional spaces, Phys. Rev. Lett. 98 (2007) 150201 [INSPIRE].
R. Easther, A.H. Guth and A. Masoumi, Counting vacua in random landscapes, arXiv:1612.05224 [INSPIRE].
S. Ferrara, R. Kallosh and A. Linde, Cosmology with nilpotent superfields, JHEP 10 (2014) 143 [arXiv:1408.4096] [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, \( \overline{D3} \) and dS, JHEP 05 (2015) 058 [arXiv:1502.07627] [INSPIRE].
R. Kallosh, F. Quevedo and A.M. Uranga, String theory realizations of the nilpotent goldstino, JHEP 12 (2015) 039 [arXiv:1507.07556] [INSPIRE].
L. Aparicio, F. Quevedo and R. Valandro, Moduli stabilisation with nilpotent goldstino: vacuum structure and SUSY breaking, JHEP 03 (2016) 036 [arXiv:1511.08105] [INSPIRE].
I. García-Etxebarria, F. Quevedo and R. Valandro, Global string embeddings for the nilpotent goldstino, JHEP 02 (2016) 148 [arXiv:1512.06926] [INSPIRE].
K. Dasgupta, M. Emelin and E. McDonough, Fermions on the antibrane: higher order interactions and spontaneously broken supersymmetry, Phys. Rev. D 95 (2017) 026003 [arXiv:1601.03409] [INSPIRE].
B. Vercnocke and T. Wrase, Constrained superfields from an anti-D3-brane in KKLT, JHEP 08 (2016) 132 [arXiv:1605.03961] [INSPIRE].
R. Kallosh, B. Vercnocke and T. Wrase, String theory origin of constrained multiplets, JHEP 09 (2016) 063 [arXiv:1606.09245] [INSPIRE].
L. Aalsma, J.P. van der Schaar and B. Vercnocke, Constrained superfields on metastable anti-D3-branes, JHEP 05 (2017) 089 [arXiv:1703.05771] [INSPIRE].
A. Westphal, De Sitter string vacua from Kähler uplifting, JHEP 03 (2007) 102 [hep-th/0611332] [INSPIRE].
Y. Sumitomo, S.-H. Henry Tye and S.S.C. Wong, Statistical distribution of the vacuum energy density in racetrack Kähler uplift models in string theory, JHEP 07 (2013) 052 [arXiv:1305.0753] [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 and Y. Mambrini, Moduli stabilization with positive vacuum energy, JHEP 10 (2006) 044 [hep-th/0607077] [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].
Z. Lalak, O.J. Eyton-Williams and R. Matyszkiewicz, F-term uplifting via consistent D-terms, JHEP 05 (2007) 085 [hep-th/0702026] [INSPIRE].
H. Abe, T. Higaki and T. Kobayashi, More about F-term uplifting, Phys. Rev. D 76 (2007) 105003 [arXiv:0707.2671] [INSPIRE].
P. Brax, A.-C. Davis, S.C. Davis, R. Jeannerot and M. Postma, Warping and F-term uplifting, JHEP 09 (2007) 125 [arXiv:0707.4583] [INSPIRE].
P. Brax, A.-C. Davis, S.C. Davis, R. Jeannerot and M. Postma, D-term uplifted racetrack inflation, JCAP 01 (2008) 008 [arXiv:0710.4876] [INSPIRE].
E. Dudas, Y. Mambrini, S. Pokorski and A. Romagnoni, Moduli stabilization with Fayet-Iliopoulos uplift, JHEP 04 (2008) 015 [arXiv:0711.4934] [INSPIRE].
D. Gallego and M. Serone, Moduli stabilization in non-supersymmetric Minkowski vacua with anomalous U(1) symmetry, JHEP 08 (2008) 025 [arXiv:0807.0190] [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].
A. Giveon, A. Katz and Z. Komargodski, Uplifted metastable vacua and gauge mediation in SQCD, JHEP 07 (2009) 099 [arXiv:0905.3387] [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. de Alwis and A. Westphal, Heterotic moduli stabilisation, JHEP 10 (2013) 199 [arXiv:1304.1809] [INSPIRE].
M. Rummel and Y. Sumitomo, De Sitter vacua from a D-term generated racetrack uplift, JHEP 01 (2015) 015 [arXiv:1407.7580] [INSPIRE].
R. Kallosh and A. Linde, Inflation and uplifting with nilpotent superfields, JCAP 01 (2015) 025 [arXiv:1408.5950] [INSPIRE].
M. Cicoli, F. Quevedo and R. Valandro, De Sitter from T-branes, JHEP 03 (2016) 141 [arXiv:1512.04558] [INSPIRE].
D. Andriot and J. Blåbäck, Refining the boundaries of the classical de Sitter landscape, JHEP 03 (2017) 102 [arXiv:1609.00385] [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].
R. Kallosh, A. Linde, B. Vercnocke and T. Wrase, Analytic classes of metastable de Sitter vacua, JHEP 10 (2014) 011 [arXiv:1406.4866] [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].
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].
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].
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].
J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the swampland, arXiv:1610.01533 [INSPIRE].
B. Freivogel and M. Kleban, Vacua morghulis, arXiv:1610.04564 [INSPIRE].
U. Danielsson and G. Dibitetto, Fate of stringy AdS vacua and the weak gravity conjecture, Phys. Rev. D 96 (2017) 026020 [arXiv:1611.01395] [INSPIRE].
T.W. Grimm and J. Louis, The effective action of N = 1 Calabi-Yau orientifolds, Nucl. Phys. B 699 (2004) 387 [hep-th/0403067] [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].
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].
R. Blumenhagen, J.P. Conlon, S. Krippendorf, S. Moster and F. Quevedo, SUSY breaking in local string/F-theory models, JHEP 09 (2009) 007 [arXiv:0906.3297] [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477] [hep-th/9906070] [INSPIRE].
M. Graña and J. Polchinski, Supersymmetric three form flux perturbations on AdS 5, Phys. Rev. D 63 (2001) 026001 [hep-th/0009211] [INSPIRE].
S.S. Gubser, Supersymmetry and F-theory realization of the deformed conifold with three form flux, hep-th/0010010 [INSPIRE].
M. Graña and J. Polchinski, Gauge/gravity duals with holomorphic dilaton, Phys. Rev. D 65 (2002) 126005 [hep-th/0106014] [INSPIRE].
P. Candelas and X. de la Ossa, Moduli space of Calabi-Yau manifolds, Nucl. Phys. B 355 (1991) 455 [INSPIRE].
C. Brodie and M.C.D. Marsh, The spectra of type IIB flux compactifications at large complex structure, JHEP 01 (2016) 037 [arXiv:1509.06761] [INSPIRE].
M.C.D. Marsh and K. Sousa, Universal properties of type IIB and F-theory flux compactifications at large complex structure, JHEP 03 (2016) 064 [arXiv:1512.08549] [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, C. Kounnas and D.V. Nanopoulos, Phenomenological SU(1, 1) supergravity, Nucl. Phys. B 241 (1984) 406 [INSPIRE].
J.R. Ellis, C. Kounnas and D.V. Nanopoulos, No scale supersymmetric GUTs, Nucl. Phys. B 247 (1984) 373 [INSPIRE].
U. Danielsson and G. Dibitetto, Type IIB on S 3 × S 3 through Q&P fluxes, JHEP 01 (2016) 057 [arXiv:1507.04476] [INSPIRE].
D. Gallego, On the effective description of large volume compactifications, JHEP 06 (2011) 087 [arXiv:1103.5469] [INSPIRE].
D. Gallego, Light field integration in SUGRA theories, Int. J. Mod. Phys. A 30 (2015) 1550003 [arXiv:1301.6177] [INSPIRE].
K. Sousa and P. Ortiz, Perturbative stability along the supersymmetric directions of the landscape, JCAP 02 (2015) 017 [arXiv:1408.6521] [INSPIRE].
M. Dine and N. Seiberg, Is the superstring weakly coupled?, Phys. Lett. B 162 (1985) 299 [INSPIRE].
F. Denef, M.R. Douglas and B. Florea, Building a better racetrack, JHEP 06 (2004) 034 [hep-th/0404257] [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].
S. Krippendorf, M.J. Dolan, A. Maharana and F. Quevedo, D-branes at toric singularities: model building, Yukawa couplings and flavour physics, JHEP 06 (2010) 092 [arXiv:1002.1790] [INSPIRE].
M.J. Dolan, S. Krippendorf and F. Quevedo, Towards a systematic construction of realistic D-brane models on a del Pezzo singularity, JHEP 10 (2011) 024 [arXiv:1106.6039] [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].
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].
M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, D3/D7 branes at singularities: constraints from global embedding and moduli stabilisation, JHEP 07 (2013) 150 [arXiv:1304.0022] [INSPIRE].
R. Blumenhagen, S. Moster and E. Plauschinn, Moduli stabilisation versus chirality for MSSM like type IIB orientifolds, JHEP 01 (2008) 058 [arXiv:0711.3389] [INSPIRE].
V.S. Kaplunovsky and J. Louis, Model independent analysis of soft terms in effective supergravity and in string theory, Phys. Lett. B 306 (1993) 269 [hep-th/9303040] [INSPIRE].
A. Brignole, L.E. Ibáñez and C. Muñoz, Towards a theory of soft terms for the supersymmetric Standard Model, Nucl. Phys. B 422 (1994) 125 [Erratum ibid. B 436 (1995) 747] [hep-ph/9308271] [INSPIRE].
S.K. Soni and H.A. Weldon, Analysis of the supersymmetry breaking induced by N = 1 supergravity theories, Phys. Lett. B 126 (1983) 215 [INSPIRE].
J.P. Conlon, D. Cremades and F. Quevedo, Kähler potentials of chiral matter fields for Calabi-Yau string compactifications, JHEP 01 (2007) 022 [hep-th/0609180] [INSPIRE].
M. Berg, D. Marsh, L. McAllister and E. Pajer, Sequestering in string compactifications, JHEP 06 (2011) 134 [arXiv:1012.1858] [INSPIRE].
L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys. B 557 (1999) 79 [hep-th/9810155] [INSPIRE].
L. Aparicio, M. Cicoli, S. Krippendorf, A. Maharana, F. Muia and F. Quevedo, Sequestered de Sitter string scenarios: soft-terms, JHEP 11 (2014) 071 [arXiv:1409.1931] [INSPIRE].
M. Berg, J.P. Conlon, D. Marsh and L.T. Witkowski, Superpotential de-sequestering in string models, JHEP 02 (2013) 018 [arXiv:1207.1103] [INSPIRE].
L.E. Ibáñez, C. Muñoz and S. Rigolin, Aspect of type-I string phenomenology, Nucl. Phys. B 553 (1999) 43 [hep-ph/9812397] [INSPIRE].
D. Lüst, P. Mayr, R. Richter and S. Stieberger, Scattering of gauge, matter and moduli fields from intersecting branes, Nucl. Phys. B 696 (2004) 205 [hep-th/0404134] [INSPIRE].
D. Lüst, S. Reffert and S. Stieberger, Flux-induced soft supersymmetry breaking in chiral type IIB orientifolds with D3/D7-branes, Nucl. Phys. B 706 (2005) 3 [hep-th/0406092] [INSPIRE].
G.D. Coughlan, W. Fischler, E.W. Kolb, S. Raby and G.G. Ross, Cosmological problems for the Polonyi potential, Phys. Lett. B 131 (1983) 59 [INSPIRE].
T. Banks, D.B. Kaplan and A.E. Nelson, Cosmological implications of dynamical supersymmetry breaking, Phys. Rev. D 49 (1994) 779 [hep-ph/9308292] [INSPIRE].
B. de Carlos, J.A. Casas, F. Quevedo and E. Roulet, Model independent properties and cosmological implications of the dilaton and moduli sectors of 4D strings, Phys. Lett. B 318 (1993) 447 [hep-ph/9308325] [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].
B. Heidenreich, L. McAllister and G. Torroba, Dynamic SU(2) structure from seven-branes, JHEP 05 (2011) 110 [arXiv:1011.3510] [INSPIRE].
J. Moritz, A. Retolaza and A. Westphal, Towards de Sitter from 10D, arXiv:1707.08678 [INSPIRE].
S. Sethi, Supersymmetry breaking by fluxes, arXiv:1709.03554 [INSPIRE].
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Gallego, D., Marsh, M.C.D., Vercnocke, B. et al. A new class of de Sitter vacua in type IIB large volume compactifications. J. High Energ. Phys. 2017, 193 (2017). https://doi.org/10.1007/JHEP10(2017)193
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DOI: https://doi.org/10.1007/JHEP10(2017)193