Abstract
We compute the flux-induced F-term potential in 4d F-theory compactifications at large complex structure. In this regime, each complex structure field splits as an axionic field plus its saxionic partner, and the classical F-term potential takes the form V = ZAB ρAρB up to exponentially-suppressed terms, with ρ depending on the fluxes and axions and Z on the saxions. We provide explicit, general expressions for Z and ρ, and from there analyse the set of flux vacua for an arbitrary number of fields. We identify two families of vacua with all complex structure fields fixed and a flux contribution to the tad- pole Nflux which is bounded. In the first and most generic one, the saxion vevs are bounded from above by a power of Nflux. In the second their vevs may be unbounded and Nflux is a product of two arbitrary integers, unlike what is claimed by the Tadpole Conjecture. We specialise to type IIB orientifolds, where both families of vacua are present, and link our analysis with previous results in the literature. We illustrate our findings with several examples.
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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].
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].
K. Becker, M. Becker and J. H. Schwarz, String theory and M-theory: a modern introduction, Cambridge University Press, Cambridge U.K. (2006).
F. Marchesano, Progress in D-brane model building, Fortsch. Phys. 55 (2007) 491 [hep-th/0702094] [INSPIRE].
F. Denef, Les Houches lectures on constructing string vacua, Les Houches 87 (2008) 483 [arXiv:0803.1194] [INSPIRE].
F. Denef, M. R. Douglas and S. Kachru, Physics of string flux compactifications, Ann. Rev. Nucl. Part. Sci. 57 (2007) 119 [hep-th/0701050] [INSPIRE].
L. E. Ibanez and A. M. Uranga, String theory and particle physics: an introduction to string phenomenology, Cambridge University Press, Cambridge U.K. (2012).
F. Quevedo, Local string models and moduli stabilisation, Mod. Phys. Lett. A 30 (2015) 1530004 [arXiv:1404.5151] [INSPIRE].
D. Baumann and L. McAllister, Inflation and string theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2015), [arXiv:1404.2601] [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, arXiv:2010.10519 [INSPIRE].
I. Bena, J. Blåbäck, M. Graña and S. Lüst, Algorithmically solving the tadpole problem, arXiv:2103.03250 [INSPIRE].
T. W. Grimm, C. Li and I. Valenzuela, Asymptotic flux compactifications and the swampland, JHEP 06 (2020) 009 [Erratum ibid. 01 (2021) 007] [arXiv:1910.09549] [INSPIRE].
T. W. Grimm, Moduli space holography and the finiteness of flux vacua, arXiv:2010.15838 [INSPIRE].
E. Palti, G. Tasinato and J. Ward, WEAKLY-coupled IIA flux compactifications, JHEP 06 (2008) 084 [arXiv:0804.1248] [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. Haack and J. Louis, M theory compactified on Calabi-Yau fourfolds with background flux, Phys. Lett. B 507 (2001) 296 [hep-th/0103068] [INSPIRE].
K. Becker and M. Becker, On graviton scattering amplitudes in M-theory, Phys. Rev. D 57 (1998) 6464 [hep-th/9712238] [INSPIRE].
A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163 [INSPIRE].
B. R. Greene, D. R. Morrison and M. R. Plesser, Mirror manifolds in higher dimension, Commun. Math. Phys. 173 (1995) 559 [hep-th/9402119] [INSPIRE].
A. P. Braun and T. Watari, The vertical, the horizontal and the rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications, JHEP 01 (2015) 047 [arXiv:1408.6167] [INSPIRE].
C. F. Cota, A. Klemm and T. Schimannek, Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds, JHEP 01 (2018) 086 [arXiv:1709.02820] [INSPIRE].
N. Cabo Bizet, A. Klemm and D. Vieira Lopes, Landscaping with fluxes and the E8 Yukawa point in F-theory, arXiv:1404.7645.
T. R. Taylor and C. Vafa, R R flux on Calabi-Yau and partial supersymmetry breaking, Phys. Lett. B 474 (2000) 130 [hep-th/9912152] [INSPIRE].
S. Bielleman, L. E. Ibáñez and I. Valenzuela, Minkowski 3-forms, flux string vacua, axion stability and naturalness, JHEP 12 (2015) 119 [arXiv:1507.06793] [INSPIRE].
F. Carta, F. Marchesano, W. Staessens and G. Zoccarato, Open string multi-branched and Kähler potentials, JHEP 09 (2016) 062 [arXiv:1606.00508] [INSPIRE].
A. Herraez, L. E. Ibáñez, F. Marchesano and G. Zoccarato, The type IIA flux potential, 4-forms and Freed-Witten anomalies, JHEP 09 (2018) 018 [arXiv:1802.05771] [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. Farakos, S. Lanza, L. Martucci and D. Sorokin, Three-forms in supergravity and flux compactifications, Eur. Phys. J. C 77 (2017) 602 [arXiv:1706.09422] [INSPIRE].
I. Bandos, F. Farakos, S. Lanza, L. Martucci and D. Sorokin, Three-forms, dualities and membranes in four-dimensional supergravity, JHEP 07 (2018) 028 [arXiv:1803.01405] [INSPIRE].
S. Lanza, F. Marchesano, L. Martucci and D. Sorokin, How many fluxes fit in an EFT?, JHEP 10 (2019) 110 [arXiv:1907.11256] [INSPIRE].
D. Escobar, F. Marchesano and W. Staessens, Type IIA flux vacua with mobile D6-branes, JHEP 01 (2019) 096 [arXiv:1811.09282] [INSPIRE].
D. Escobar, F. Marchesano and W. Staessens, Type IIA flux vacua and α′-corrections, JHEP 06 (2019) 129 [arXiv:1812.08735] [INSPIRE].
O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160].
F. Marchesano and J. Quirant, A landscape of AdS flux vacua, JHEP 12 (2019) 110 [arXiv:1908.11386] [INSPIRE].
I. Valenzuela, Backreaction issues in axion monodromy and Minkowski 4-forms, JHEP 06 (2017) 098 [arXiv:1611.00394] [INSPIRE].
T. W. Grimm and C. Li, Universal axion backreaction in flux compactifications, JHEP 06 (2021) 067 [arXiv:2012.08272] [INSPIRE].
E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills theories with local supersymmetry: lagrangian, transformation laws and super-Higgs effect, Nucl. Phys. B 212 (1983) 413 [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].
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].
A. Gerhardus and H. Jockers, Quantum periods of Calabi-Yau fourfolds, Nucl. Phys. B 913 (2016) 425 [arXiv:1604.05325] [INSPIRE].
F. Denef, M. R. Douglas, B. Florea, A. Grassi and S. Kachru, Fixing all moduli in a simple F-theory compactification, Adv. Theor. Math. Phys. 9 (2005) 861 [hep-th/0503124] [INSPIRE].
Y. Honma and H. Otsuka, On the flux Vacua in F-theory compactifications, Phys. Lett. B 774 (2017) 225 [arXiv:1706.09417] [INSPIRE].
J. J. Blanco-Pillado, K. Sousa, M. A. Urkiola and J. M. Wachter, Towards a complete mass spectrum of type- IIB flux vacua at large complex structure, JHEP 04 (2021) 149 [arXiv:2007.10381] [INSPIRE].
P. Shukla, Dictionary for the type II nongeometric flux compactifications, Phys. Rev. D 103 (2021) 086009 [arXiv:1909.07391].
M. Demirtas, M. Kim, L. Mcallister and J. Moritz, Vacua with small flux superpotential, Phys. Rev. Lett. 124 (2020) 211603 [arXiv:1912.10047] [INSPIRE].
J. J. Blanco-Pillado, K. Sousa, M. A. Urkiola and J. M. Wachter, Universal class of type-IIB flux vacua with analytic mass spectrum, Phys. Rev. D 103 (2021) 106006 [arXiv:2011.13953] [INSPIRE].
P. Betzler and E. Plauschinn, Type IIB flux vacua and tadpole cancellation, Fortsch. Phys. 67 (2019) 1900065 [arXiv:1905.08823] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Emergent strings from infinite distance limits, arXiv:1910.01135 [INSPIRE].
E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].
A. Collinucci and R. Savelli, On flux quantization in F-theory, JHEP 02 (2012) 015 [arXiv:1011.6388] [INSPIRE].
P. Mayr, Mirror symmetry, N = 1 superpotentials and tensionless strings on Calabi-Yau four folds, Nucl. Phys. B 494 (1997) 489 [hep-th/9610162] [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].
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].
J. Gomis, F. Marchesano and D. Mateos, An open string landscape, JHEP 11 (2005) 021 [hep-th/0506179] [INSPIRE].
Y. Honma and H. Otsuka, Small flux superpotential in F-theory compactifications, Phys. Rev. D 103 (2021) 126022 [arXiv:2103.03003] [INSPIRE].
T. D. Dimofte, Type IIB flux vacua at large complex structure, JHEP 09 (2008) 064 [arXiv:0806.0001] [INSPIRE].
B. Bastian, T. W. Grimm and D. van de Heisteeg, Modelling general asymptotic Calabi-Yau periods, arXiv:2105.02232 [INSPIRE].
M. Demirtas, M. Kim, L. McAllister and J. Moritz, Conifold vacua with small flux superpotential, Fortsch. Phys. 68 (2020) 2000085 [arXiv:2009.03312] [INSPIRE].
R. Álvarez-García, R. Blumenhagen, M. Brinkmann and L. Schlechter, Small flux superpotentials for Type IIB flux vacua close to a conifold, arXiv:2009.03325 [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Modular fluxes, elliptic genera, and weak gravity conjectures in four dimensions, JHEP 08 (2019) 104 [arXiv:1901.08065] [INSPIRE].
D. Klaewer, S.-J. Lee, T. Weigand and M. Wiesner, Quantum corrections in 4d N = 1 infinite distance limits and the weak gravity conjecture, JHEP 03 (2021) 252 [arXiv:2011.00024] [INSPIRE].
J. Halverson, H. Jockers, J. M. Lapan and D. R. Morrison, Perturbative corrections to Kähler moduli spaces, Commun. Math. Phys. 333 (2015) 1563 [arXiv:1308.2157] [INSPIRE].
Y. Honma and M. Manabe, Exact Kähler potential for Calabi-Yau fourfolds, JHEP 05 (2013) 102 [arXiv:1302.3760] [INSPIRE].
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Marchesano, F., Prieto, D. & Wiesner, M. F-theory flux vacua at large complex structure. J. High Energ. Phys. 2021, 77 (2021). https://doi.org/10.1007/JHEP08(2021)077
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DOI: https://doi.org/10.1007/JHEP08(2021)077