Abstract
The tadpole conjecture by Bena, Blåbäck, Graña and Lüst effectively states that for string-theory compactifications with a large number of complex-structure moduli, not all of these moduli can be stabilized by fluxes. In this note we study this conjecture in the large complex-structure regime using statistical data obtained by Demirtas, Long, McAllister and Stillman for the Kreuzer-Skarke list. We estimate a lower bound on the flux number in type IIB Calabi-Yau orientifold compactifications at large complex-structure and for large h2,1, and our results support the tadpole conjecture in this regime.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
A.N. Schellekens, Big Numbers in String Theory, arXiv:1601.02462 [INSPIRE].
W. Lerche, D. Lüst and A.N. Schellekens, Chiral Four-Dimensional Heterotic Strings from Selfdual Lattices, Nucl. Phys. B 287 (1987) 477 [INSPIRE].
W. Taylor and Y.-N. Wang, The F-theory geometry with most flux vacua, JHEP 12 (2015) 164 [arXiv:1511.03209] [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].
T.W. Grimm, Moduli space holography and the finiteness of flux vacua, JHEP 10 (2021) 153 [arXiv:2010.15838] [INSPIRE].
B. Bakker, T.W. Grimm, C. Schnell and J. Tsimerman, to appear.
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].
I. Bena, E. Dudas, M. Graña and S. Lüst, Uplifting Runaways, Fortsch. Phys. 67 (2019) 1800100 [arXiv:1809.06861] [INSPIRE].
P. Betzler and E. Plauschinn, Type IIB flux vacua and tadpole cancellation, Fortsch. Phys. 67 (2019) 1900065 [arXiv:1905.08823] [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].
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, 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].
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].
E. Plauschinn, The Generalized Green-Schwarz Mechanism for Type IIB Orientifolds with D3- and D7-branes, JHEP 05 (2009) 062 [arXiv:0811.2804] [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].
W. Schmid, Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973) 211.
E. Cattani, A. Kaplan and W. Schmid, Degeneration of Hodge Structures, Annals Math. 123 (1986) 457.
M. Demirtas, C. Long, L. McAllister and M. Stillman, The Kreuzer-Skarke Axiverse, JHEP 04 (2020) 138 [arXiv:1808.01282] [INSPIRE].
M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four-dimensions, Adv. Theor. Math. Phys. 4 (2000) 1209 [hep-th/0002240] [INSPIRE].
M. Cicoli, D. Ciupke, C. Mayrhofer and P. Shukla, A Geometrical Upper Bound on the Inflaton Range, JHEP 05 (2018) 001 [arXiv:1801.05434] [INSPIRE].
A. Joshi and A. Klemm, Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds, JHEP 08 (2019) 086 [arXiv:1903.00596] [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: 2109.00029
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
Plauschinn, E. The tadpole conjecture at large complex-structure. J. High Energ. Phys. 2022, 206 (2022). https://doi.org/10.1007/JHEP02(2022)206
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2022)206