Abstract
Recent work on flux compactifications suggests that the tadpole constraint generically allows only a limited number of complex structure moduli to become massive, i.e., be stabilized at quadratic order in the spacetime superpotential. We study the effects of higher-order terms systematically around the Fermat point in the 19 Landau-Ginzburg model. This model lives at strong coupling and features no Kähler moduli. We show that indeed massless fields can be stabilized in this fashion. We observe that, depending on the flux, this mechanism is more effective when the number of initially massless fields is large. These findings are compatible with both the tadpole conjecture and the massless Minkowski conjecture. Along the way, we complete the classification of integral flux vectors with small tadpole contribution. Thereby we are closing in on a future complete understanding of all possible flux configurations in the 19 Landau-Ginzburg model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Grana, 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].
R. Blumenhagen, B. Kors, D. Lust and S. Stieberger, Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [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, Y.-C. Chung and G.-Y. Guo, Metastable Flux Configurations and de Sitter Spaces, Nucl. Phys. B 790 (2008) 240 [arXiv:0706.2502] [INSPIRE].
K. Becker, M. Becker and J. Walcher, Runaway in the Landscape, Phys. Rev. D 76 (2007) 106002 [arXiv:0706.0514] [INSPIRE].
J. Bardzell et al., Type IIB flux compactifications with h1,1 = 0, JHEP 06 (2022) 166 [arXiv:2203.15818] [INSPIRE].
K. Becker, E. Gonzalo, J. Walcher and T. Wrase, Fluxes, vacua, and tadpoles meet Landau-Ginzburg and Fermat, JHEP 12 (2022) 083 [arXiv:2210.03706] [INSPIRE].
S. Cremonini et al., On asymptotic dark energy in string theory, JHEP 09 (2023) 075 [arXiv:2306.15714] [INSPIRE].
K. Becker, N. Brady and A. Sengupta, On fluxes in the 19 Landau-Ginzburg model, JHEP 11 (2023) 152 [arXiv:2310.00770] [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].
A. Giryavets, S. Kachru, P.K. Tripathy and S.P. Trivedi, Flux compactifications on Calabi-Yau threefolds, JHEP 04 (2004) 003 [hep-th/0312104] [INSPIRE].
F. Denef, M.R. Douglas and B. Florea, Building a better racetrack, JHEP 06 (2004) 034 [hep-th/0404257] [INSPIRE].
F. Denef et al., Fixing all moduli in a simple f-theory compactification, Adv. Theor. Math. Phys. 9 (2005) 861 [hep-th/0503124] [INSPIRE].
A.P. Braun and R. Valandro, G4 flux, algebraic cycles and complex structure moduli stabilization, JHEP 01 (2021) 207 [arXiv:2009.11873] [INSPIRE].
I. Bena, J. Blåbäck, M. Graña and S. Lüst, The tadpole problem, JHEP 11 (2021) 223 [arXiv:2010.10519] [INSPIRE].
I. Bena, J. Blåbäck, M. Graña and S. Lüst, Algorithmically Solving the Tadpole Problem, Adv. Appl. Clifford Algebras 32 (2022) 7 [arXiv:2103.03250] [INSPIRE].
I. Bena, C. Brodie and M. Graña, D7 moduli stabilization: the tadpole menace, JHEP 01 (2022) 138 [arXiv:2112.00013] [INSPIRE].
E. Plauschinn, The tadpole conjecture at large complex-structure, JHEP 02 (2022) 206 [arXiv:2109.00029] [INSPIRE].
S. Lüst, Large complex structure flux vacua of IIB and the Tadpole Conjecture, arXiv:2109.05033 [INSPIRE].
F. Marchesano, D. Prieto and M. Wiesner, F-theory flux vacua at large complex structure, JHEP 08 (2021) 077 [arXiv:2105.09326] [INSPIRE].
M. Graña et al., The tadpole conjecture in asymptotic limits, JHEP 08 (2022) 237 [arXiv:2204.05331] [INSPIRE].
K. Tsagkaris and E. Plauschinn, Moduli stabilization in type IIB orientifolds at h2,1 = 50, JHEP 03 (2023) 049 [arXiv:2207.13721] [INSPIRE].
T. Coudarchet, F. Marchesano, D. Prieto and M.A. Urkiola, Symmetric fluxes and small tadpoles, JHEP 08 (2023) 016 [arXiv:2304.04789] [INSPIRE].
A.P. Braun et al., Tadpoles and gauge symmetries, JHEP 08 (2023) 134 [arXiv:2304.06751] [INSPIRE].
S. Lüst and M. Wiesner, The tadpole conjecture in the interior of moduli space, JHEP 12 (2023) 029 [arXiv:2211.05128] [INSPIRE].
A.P. Braun, H. Fortin, D.L. Garcia and R.V. Loyola, More on G-flux and general hodge cycles on the Fermat sextic, JHEP 06 (2024) 046 [arXiv:2401.00470] [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].
K. Ishiguro and H. Otsuka, Sharpening the boundaries between flux landscape and swampland by tadpole charge, JHEP 12 (2021) 017 [arXiv:2104.15030] [INSPIRE].
D. Andriot, L. Horer and P. Marconnet, Exploring the landscape of (anti-) de Sitter and Minkowski solutions: group manifolds, stability and scale separation, JHEP 08 (2022) 109 [Erratum ibid. 09 (2022) 184] [arXiv:2204.05327] [INSPIRE].
C. Vafa, String Vacua and Orbifoldized L-G Models, Mod. Phys. Lett. A 4 (1989) 1169 [INSPIRE].
C. Vafa and N.P. Warner, Catastrophes and the Classification of Conformal Theories, Phys. Lett. B 218 (1989) 51 [INSPIRE].
K. Hori, A. Iqbal and C. Vafa, D-branes and mirror symmetry, hep-th/0005247 [INSPIRE].
I. Brunner, M.R. Douglas, A.E. Lawrence and C. Romelsberger, D-branes on the quintic, JHEP 08 (2000) 015 [hep-th/9906200] [INSPIRE].
S. Cecotti and C. Vafa, Topological antitopological fusion, Nucl. Phys. B 367 (1991) 359 [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [hep-th/9906070] [INSPIRE].
K. Hori and J. Walcher, D-brane Categories for Orientifolds: The Landau-Ginzburg Case, JHEP 04 (2008) 030 [hep-th/0606179] [INSPIRE].
F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP 05 (2004) 072 [hep-th/0404116] [INSPIRE].
T.W. Grimm and J. Louis, The effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B 718 (2005) 153 [hep-th/0412277] [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].
M. Kim, D-instanton superpotential in string theory, JHEP 03 (2022) 054 [arXiv:2201.04634] [INSPIRE].
T.W. Grimm and D. van de Heisteeg, Exact Flux Vacua, Symmetries, and the Structure of the Landscape, arXiv:2404.12422 [INSPIRE].
Acknowledgments
We would like to thank James Gray for useful discussions, and Mariana Gra na for valuable feedback on an initial draft. The work of KB and AS is supported in part by the NSF grant PHY-2112859. MR acknowledges the support of the Dr. Hyo Sang Lee Graduate Fellowship from the College of Arts and Sciences at Lehigh University. The work of MR and TW is supported in part by the NSF grant PHY-2210271. This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP). JW thanks the International Centre for Mathematical Sciences, Edinburgh, for support and hospitality during the ICMS Visiting Fellows programme where this work was completed. This work was supported by EPSRC grant EP/V521905/1. This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2181/1 — 390900948 (the Heidelberg STRUCTURES Excellence Cluster).
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: 2406.03435
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
Becker, K., Rajaguru, M., Sengupta, A. et al. Stabilizing massless fields with fluxes in Landau-Ginzburg models. J. High Energ. Phys. 2024, 69 (2024). https://doi.org/10.1007/JHEP08(2024)069
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2024)069