Abstract
String theory has no parameter except the string scale MS, so the Planck scale MPl, the supersymmetry-breaking scale , the electroweak scale mEW as well as the vacuum energy density (cosmological constant) Λ are to be determined dynamically at any local minimum solution in the string theory landscape. Here we consider a model that links the supersymmetric electroweak phenomenology (bottom up) to the string theory motivated flux compactification approach (top down). In this model, supersymmetry is broken by a combination of the racetrack Kähler uplift mechanism, which naturally allows an exponentially small positive Λ in a local minimum, and the anti-D3-brane in the KKLT scenario. In the absence of the Higgs doublets from the supersymmetric standard model, one has either a small Λ or a big enough
, but not both. The introduction of the Higgs fields (with their soft terms) allows a small Λ and a big enough
simultaneously. Since an exponentially small Λ is statistically preferred (as the properly normalized probability distribution P(Λ) diverges at Λ = 0+), identifying the observed Λobs to the median value Λ50% yields mEW ∼ 100 GeV. We also find that the warped anti-D3-brane tension has a SUSY-breaking scale
∼ 100 mEW while the SUSY-breaking scale that directly correlates with the Higgs fields in the visible sector is
≃ mEW.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.P. Martin, A Supersymmetry primer, in Advanced Series on Directions in High Energy Physics. Vol. 21: Perspectives on supersymmetry. Vol. 2, G.L. Kane eds., World Scientific, New York U.S.A. (2010), pg. 1 [hep-ph/9709356] [INSPIRE].
S. Weinberg, The quantum theory of fields. Vol. 3: Supersymmetry, Cambridge University Press, Cambridge U.K. (2013).
H. Baer and X. Tata, Weak scale supersymmetry: From superfields to scattering events, Cambridge University Press, Cambridge U.K. (2006).
R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [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].
M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].
K. Becker, M. Becker and J. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press, Cambridge U.K. (2006).
L.E. Ibanez and A.M. Uranga, String theory and particle physics: An introduction to string phenomenology, Cambridge University Press, Cambridge U.K. (2012).
Y. Sumitomo, S.H. Tye and S.S.C. Wong, Statistical Distribution of the Vacuum Energy Density in Racetrack K\”ahler Uplift Models in String Theory, JHEP 07 (2013) 052 [arXiv:1305.0753] [INSPIRE].
N.V. Krasnikov, On Supersymmetry Breaking in Superstring Theories, Phys. Lett. B 193 (1987) 37 [INSPIRE].
T.R. Taylor, Dilaton, gaugino condensation and supersymmetry breaking, Phys. Lett. B 252 (1990) 59 [INSPIRE].
F. Denef, M.R. Douglas and B. Florea, Building a better racetrack, JHEP 06 (2004) 034 [hep-th/0404257] [INSPIRE].
V. Balasubramanian and P. Berglund, Stringy corrections to Kähler potentials, SUSY breaking, and the cosmological constant problem, JHEP 11 (2004) 085 [hep-th/0408054] [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].
S. de Alwis and K. Givens, Physical Vacua in IIB Compactifications with a Single Kähler Modulus, JHEP 10 (2011) 109 [arXiv:1106.0759] [INSPIRE].
Y. Sumitomo and S.H.H. Tye, A Stringy Mechanism for A Small Cosmological Constant — Multi-Moduli Cases, JCAP 02 (2013) 006 [arXiv:1209.5086] [INSPIRE].
J. Louis, M. Rummel, R. Valandro and A. Westphal, Building an explicit de Sitter, JHEP 10 (2012) 163 [arXiv:1208.3208] [INSPIRE].
M. Dine and N. Seiberg, Is the Superstring Weakly Coupled?, Phys. Lett. B 162 (1985) 299 [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
V. Novikov, M.A. Shifman, A. Vainshtein and V.I. Zakharov, Instanton Effects in Supersymmetric Theories, Nucl. Phys. B 229 (1983) 407.
V.A. Novikov, M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Supersymmetry Transformations of Instantons, Nucl. Phys. B 229 (1983) 394 [INSPIRE].
S. Ferrara, L. Girardello and H.P. Nilles, Breakdown of Local Supersymmetry Through Gauge Fermion Condensates, Phys. Lett. B 125 (1983) 457 [INSPIRE].
M. Dine, R. Rohm, N. Seiberg and E. Witten, Gluino Condensation in Superstring Models, Phys. Lett. B 156 (1985) 55 [INSPIRE].
J.P. Derendinger, L.E. Ibáñez and H.P. Nilles, On the Low-Energy d = 4, N = 1 Supergravity Theory Extracted from the d = 10, N = 1 Superstring, Phys. Lett. B 155 (1985) 65 [INSPIRE].
M.A. Shifman and A.I. Vainshtein, On Gluino Condensation in Supersymmetric Gauge Theories. SU(N) and O(N) Groups, Sov. Phys. JETP 66 (1987) 1100 [INSPIRE].
L. Görlich, S. Kachru, P.K. Tripathy and S.P. Trivedi, Gaugino condensation and nonperturbative superpotentials in flux compactifications, JHEP 12 (2004) 074 [hep-th/0407130] [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].
S. Andriolo, S.Y. Li and S.-H.H. Tye, The Cosmological Constant and the Electroweak Scale, JHEP 10 (2019) 212 [arXiv:1812.04873] [INSPIRE].
S.H.H. 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].
L. Girardello and M.T. Grisaru, Soft Breaking of Supersymmetry, Nucl. Phys. B 194 (1982) 65 [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde, J.M. Maldacena, L.P. McAllister and S.P. Trivedi, Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].
S. Kachru, M. Kim, L. McAllister and M. Zimet, de Sitter Vacua from Ten Dimensions, arXiv:1908.04788 [INSPIRE].
M.P. Garcia del Moral, S. Parameswaran, N. Quiroz and I. Zavala, Anti-D3 branes and moduli in non-linear supergravity, JHEP 10 (2017) 185 [arXiv:1707.07059] [INSPIRE].
N. Cribiori, C. Roupec, T. Wrase and Y. Yamada, Supersymmetric anti-D3-brane action in the Kachru-Kallosh-Linde-Trivedi setup, Phys. Rev. D 100 (2019) 066001 [arXiv:1906.07727] [INSPIRE].
S. Parameswaran and F. Tonioni, Non-supersymmetric String Models from Anti-D3-/D7-branes in Strongly Warped Throats, arXiv:2007.11333 [INSPIRE].
E.W. Kolb and M.S. Turner, The Early Universe, Nature 294 (1981) 521 [INSPIRE].
D.J.E. Marsh, Axion Cosmology, Phys. Rept. 643 (2016) 1 [arXiv:1510.07633] [INSPIRE].
S. Andriolo, S.Y. Li and S.-H.H. Tye, String Landscape and Fermion Masses, Phys. Rev. D 101 (2020) 066005 [arXiv:1902.06608] [INSPIRE].
Y. Hamada, A. Hebecker, G. Shiu and P. Soler, Understanding KKLT from a 10d perspective, JHEP 06 (2019) 019 [arXiv:1902.01410] [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].
D. Baumann and L. McAllister, Inflation and String Theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press (5, 2015), https://doi.org/10.1017/CBO9781316105733 [arXiv:1404.2601] [INSPIRE].
P. Candelas and H. Skarke, F theory, SO(32) and toric geometry, Phys. Lett. B 413 (1997) 63 [hep-th/9706226] [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].
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [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].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
G.R. Dvali and S.H. Tye, Brane inflation, Phys. Lett. B 450 (1999) 72 [hep-ph/9812483] [INSPIRE].
G.R. Dvali, Q. Shafi and S. Solganik, D-brane inflation, in 4th European Meeting From the Planck Scale to the Electroweak Scale (Planck 2001), Toulon France (2001) [hep-th/0105203] [INSPIRE].
C.P. Burgess, M. Majumdar, D. Nolte, F. Quevedo, G. Rajesh and R.-J. Zhang, The Inflationary brane anti-brane universe, JHEP 07 (2001) 047 [hep-th/0105204] [INSPIRE].
F. Koyama, Y. Tachikawa and T. Watari, Supergravity analysis of hybrid inflation model from D3-D7 system, Phys. Rev. D 69 (2004) 106001 [Erratum ibid. 70 (2004) 129907] [hep-th/0311191] [INSPIRE].
K. Dasgupta, J.P. Hsu, R. Kallosh, A.D. Linde and M. Zagermann, D3/D7 brane inflation and semilocal strings, JHEP 08 (2004) 030 [hep-th/0405247] [INSPIRE].
E. Dudas and S. Lüst, An update on moduli stabilization with antibrane uplift, arXiv:1912.09948 [INSPIRE].
K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and alpha-prime corrections to flux induced potentials, JHEP 06 (2002) 060 [hep-th/0204254] [INSPIRE].
D.J. Gross and E. Witten, Superstring Modifications of Einstein’s Equations, Nucl. Phys. B 277 (1986) 1 [INSPIRE].
K. Choi, A. Falkowski, H.P. Nilles and M. Olechowski, Soft supersymmetry breaking in KKLT flux compactification, Nucl. Phys. B 718 (2005) 113 [hep-th/0503216] [INSPIRE].
D. Lüst, S. Reffert, W. Schulgin and S. Stieberger, Moduli stabilization in type IIB orientifolds (I): Orbifold limits, Nucl. Phys. B 766 (2007) 68 [hep-th/0506090] [INSPIRE].
D. Lüst, S. Reffert, E. Scheidegger, W. Schulgin and S. Stieberger, Moduli Stabilization in Type IIB Orientifolds (II), Nucl. Phys. B 766 (2007) 178 [hep-th/0609013] [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].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2006.16620
Rights and permissions
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.
About this article
Cite this article
Qiu, YC., Tye, SH.H. Linking the supersymmetric standard model to the cosmological constant. J. High Energ. Phys. 2021, 117 (2021). https://doi.org/10.1007/JHEP01(2021)117
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2021)117