Abstract
We investigate the vacuum structure of four-dimensional effective theory arising from Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold, corresponding to a T-dual of the DeWolfe-Giryavets-Kachru-Taylor model in Type IIA flux compactifications. By analyzing the vacuum structure of this interesting corner of string landscape, it turns out that there exist perturbatively unstable de Sitter (dS) vacua in addition to supersymmetric and non-supersymmetric anti-de Sitter vacua. On the other hand, the stable dS vacua appearing in the low-energy effective action violate the tadpole cancellation condition, indicating a strong correlation between the existence of dS vacua and the flux-induced D3-brane charge (tadpole charge). We also find analytically that the tadpole charge constrained by the tadpole cancellation condition emerges in the scalar potential in a nontrivial way. Thus, the tadpole charge would restrict the existence of stable dS vacua, and this fact underlies the statement of the dS conjecture. Furthermore, our analytical and numerical results exhibit that distributions of \( \mathcal{O}(1) \) parameters in expressions of several swampland conjectures peak at specific values.
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References
C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [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].
U. H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys. D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
D. Andriot, On the de Sitter swampland criterion, Phys. Lett. B 785 (2018) 570 [arXiv:1806.10999] [INSPIRE].
S. K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, JHEP 11 (2019) 075 [arXiv:1807.05193] [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].
P. G. Cámara, A. Font and L. E. Ibáñez, Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold, JHEP 09 (2005) 013 [hep-th/0506066] [INSPIRE].
O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [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].
D. Junghans, Weakly Coupled de Sitter Vacua with Fluxes and the Swampland, JHEP 03 (2019) 150 [arXiv:1811.06990] [INSPIRE].
F. Marchesano, D. Prieto, J. Quirant and P. Shukla, Systematics of Type IIA moduli stabilisation, JHEP 11 (2020) 113 [arXiv:2007.00672] [INSPIRE].
F. F. Gautason, V. Van Hemelryck and T. Van Riet, The Tension between 10D Supergravity and dS Uplifts, Fortsch. Phys. 67 (2019) 1800091 [arXiv:1810.08518] [INSPIRE].
D. Lüst, E. Palti and C. Vafa, AdS and the Swampland, Phys. Lett. B 797 (2019) 134867 [arXiv:1906.05225] [INSPIRE].
F. Marchesano and J. Quirant, A Landscape of AdS Flux Vacua, JHEP 12 (2019) 110 [arXiv:1908.11386] [INSPIRE].
R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [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].
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. Berg, M. Haack and B. Körs, On volume stabilization by quantum corrections, Phys. Rev. Lett. 96 (2006) 021601 [hep-th/0508171] [INSPIRE].
T. Kobayashi, N. Omoto, H. Otsuka and T. H. Tatsuishi, Radiative Kähler moduli stabilization, Phys. Rev. D 97 (2018) 106006 [arXiv:1711.10274] [INSPIRE].
I. Bena, E. Dudas, M. Graña and S. Lüst, Uplifting Runaways, Fortsch. Phys. 67 (2019) 1800100 [arXiv:1809.06861] [INSPIRE].
R. Blumenhagen, D. Kläwer and L. Schlechter, Swampland Variations on a Theme by KKLT, JHEP 05 (2019) 152 [arXiv:1902.07724] [INSPIRE].
X. Gao, A. Hebecker and D. Junghans, Control issues of KKLT, Fortsch. Phys. 68 (2020) 2000089 [arXiv:2009.03914] [INSPIRE].
P. Candelas, E. Derrick and L. Parkes, Generalized Calabi-Yau manifolds and the mirror of a rigid manifold, Nucl. Phys. B 407 (1993) 115 [hep-th/9304045] [INSPIRE].
P. Shukla, Rigid nongeometric orientifolds and the swampland, Phys. Rev. D 103 (2021) 086010 [arXiv:1909.10993] [INSPIRE].
K. Becker, M. Becker, C. Vafa and J. Walcher, Moduli Stabilization in Non-Geometric Backgrounds, Nucl. Phys. B 770 (2007) 1 [hep-th/0611001] [INSPIRE].
K. Becker, M. Becker and J. Walcher, Runaway in the Landscape, Phys. Rev. D 76 (2007) 106002 [arXiv:0706.0514] [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. 608 (2001) 477] [hep-th/9906070] [INSPIRE].
M. Atiyah, R. Bott and L. Gårding, Lacunas for hyperbolic differential operators with constant coefficients. II, Acta Math. 131 (1973) 145.
P. Candelas, Yukawa Couplings Between (2, 1) Forms, Nucl. Phys. B 298 (1988) 458 [INSPIRE].
P. A. Griffiths, On the Periods of Certain Rational Integrals: I, Annals Math. 90 (1969) 460.
P. A. Griffiths, On the Periods of Certain Rational Integrals: II, Annals Math. 90 (1969) 496.
A. Giveon and D.-J. Smit, Symmetries on the Moduli Space of (2, 2) Superstring Vacua, Nucl. Phys. B 349 (1991) 168 [INSPIRE].
C. Vafa, String Vacua and Orbifoldized L-G Models, Mod. Phys. Lett. A 4 (1989) 1169 [INSPIRE].
A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163 [INSPIRE].
P. Candelas and X. de la Ossa, Moduli Space of Calabi-Yau Manifolds, Nucl. Phys. B 355 (1991) 455 [INSPIRE].
K. Ishiguro, T. Kobayashi and H. Otsuka, Spontaneous CP-violation and symplectic modular symmetry in Calabi-Yau compactifications, Nucl. Phys. B 973 (2021) 115598 [arXiv:2010.10782] [INSPIRE].
K. Kodaira, Complex manifolds and deformation of complex structures Springer (2006) [DOI].
E. Plauschinn, Moduli Stabilization with Non-Geometric Fluxes — Comments on Tadpole Contributions and de-Sitter Vacua, Fortsch. Phys. 69 (2021) 2100003 [arXiv:2011.08227] [INSPIRE].
D. Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge, U.K. (2012) [DOI].
F. F. Gautason, M. Schillo, T. Van Riet and M. Williams, Remarks on scale separation in flux vacua, JHEP 03 (2016) 061 [arXiv:1512.00457] [INSPIRE].
R. Blumenhagen, M. Brinkmann and A. Makridou, Quantum Log-Corrections to Swampland Conjectures, JHEP 02 (2020) 064 [arXiv:1910.10185] [INSPIRE].
K. Becker, Y.-C. Chung and G.-y. Guo, Metastable Flux Configurations and de Sitter Spaces, Nucl. Phys. B 790 (2008) 240 [arXiv:0706.2502] [INSPIRE].
A. Strominger and E. Witten, New Manifolds for Superstring Compactification, Commun. Math. Phys. 101 (1985) 341 [INSPIRE].
K. Ishiguro, T. Kobayashi and H. Otsuka, Hierarchical structure of physical Yukawa couplings from matter field Kähler metric, JHEP 07 (2021) 064 [arXiv:2103.10240] [INSPIRE].
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Ishiguro, K., Otsuka, H. Sharpening the boundaries between flux landscape and swampland by tadpole charge. J. High Energ. Phys. 2021, 17 (2021). https://doi.org/10.1007/JHEP12(2021)017
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DOI: https://doi.org/10.1007/JHEP12(2021)017