Abstract
We initiate the systematic study of flux scalar potentials and their vacua by using asymptotic Hodge theory. To begin with, we consider F-theory compactifications on Calabi-Yau fourfolds with four-form flux. We argue that a classification of all scalar potentials can be performed when focusing on regions in the field space in which one or several fields are large and close to a boundary. To exemplify the constraints on such asymptotic flux compactifications, we explicitly determine this classification for situations in which two complex structure moduli are taken to be large. Our classification captures, for example, the weak string coupling limit and the large complex structure limit. We then show that none of these scalar potentials admits de Sitter critical points at parametric control, formulating a new no-go theorem valid beyond weak string coupling. We also check that the recently proposed asymptotic de Sitter conjecture is satisfied near any infinite distance boundary. Extending this strategy further, we generally identify the type of fluxes that induce an infinite series of Anti-de Sitter critical points, thereby generalizing the well-known Type IIA settings. Finally, we argue that also the large field dynamics of any axion in complex structure moduli space is universally constrained. Displacing such an axion by large field values will generally lead to severe backreaction effects destabilizing other directions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
04 January 2021
In the original paper a wrong affiliation has been assigned to author Chongchuo Li during the typesetting.
References
M. Dine and N. Seiberg, Is the superstring weakly coupled?, Phys. Lett. B 162 (1985) 299.
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].
R. Flauger, S. Paban, D. Robbins and T. Wrase, Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes, Phys. Rev. D 79 (2009) 086011 [arXiv:0812.3886] [INSPIRE].
T. Wrase and M. Zagermann, On classical de Sitter vacua in string theory, Fortsch. Phys. 58 (2010) 906 [arXiv:1003.0029] [INSPIRE].
A. Banlaki, A. Chowdhury, C. Roupec and T. Wrase, Scaling limits of dS vacua and the swampland, JHEP 03 (2019) 065 [arXiv:1811.07880] [INSPIRE].
C. Roupec and T. Wrase, de Sitter extrema and the swampland, Fortsch. Phys. 67 (2019) 1800082 [arXiv:1807.09538] [INSPIRE].
D. Junghans, Weakly coupled de Sitter vacua with fluxes and the swampland, JHEP 03 (2019) 150 [arXiv:1811.06990] [INSPIRE].
D. Andriot, Open problems on classical de Sitter solutions, Fortsch. Phys. 67 (2019) 1900026 [arXiv:1902.10093] [INSPIRE].
E. Palti, The swampland: introduction and review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [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].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, De Sitter space and the swampland, arXiv:1806.08362 [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on slow roll and the de Sitter swampland, JHEP 11 (2019) 075 [arXiv:1807.05193] [INSPIRE].
C. Vafa, The String landscape and the swampland, hep-th/0509212 [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].
T.W. Grimm, E. Palti and I. Valenzuela, Infinite distances in field space and massless towers of states, JHEP 08 (2018) 143 [arXiv:1802.08264] [INSPIRE].
T.W. Grimm, C. Li and E. Palti, Infinite distance networks in field space and charge orbits, JHEP 03 (2019) 016 [arXiv:1811.02571] [INSPIRE].
P. Corvilain, T.W. Grimm and I. Valenzuela, The swampland distance conjecture for Kähler moduli, JHEP 08 (2019) 075 [arXiv:1812.07548] [INSPIRE].
O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].
F. Baume and E. Palti, Backreacted axion field ranges in string theory, JHEP 08 (2016) 043 [arXiv:1602.06517] [INSPIRE].
I. Valenzuela, Backreaction issues in axion monodromy and Minkowski 4-forms, JHEP 06 (2017) 098 [arXiv:1611.00394] [INSPIRE].
R. Blumenhagen, I. Valenzuela and F. Wolf, The swampland conjecture and F-term axion monodromy inflation, JHEP 07 (2017) 145 [arXiv:1703.05776] [INSPIRE].
D. Klaewer and E. Palti, Super-Planckian spatial field variations and quantum gravity, JHEP 01 (2017) 088 [arXiv:1610.00010] [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].
F. Denef, Les Houches lectures on constructing string vacua, Les Houches 87 (2008) 483 [arXiv:0803.1194] [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].
E. Cattani, A. Kaplan and W. Schmid, Degeneration of Hodge structures, Ann. Math. 123 (1986) 457.
M. Kerr, G.J. Pearlstein and C. Robles, Polarized relations on horizontal SL(2)’s, Doc. Math. 24 (2019) 1295.
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].
A. Font, A. Herráez and L.E. Ibáñez, The swampland distance conjecture and towers of tensionless branes, JHEP 08 (2019) 044 [arXiv:1904.05379] [INSPIRE].
T.W. Grimm and D. Van De Heisteeg, Infinite distances and the axion weak gravity conjecture, JHEP 03 (2020) 020 [arXiv:1905.00901] [INSPIRE].
E. Palti, On natural inflation and moduli stabilisation in string theory, JHEP 10 (2015) 188 [arXiv:1508.00009] [INSPIRE].
S. Bielleman et al., Higgs-otic inflation and moduli stabilization, JHEP 02 (2017) 073 [arXiv:1611.07084] [INSPIRE].
E. Palti, The weak gravity conjecture and scalar fields, JHEP 08 (2017) 034 [arXiv:1705.04328] [INSPIRE].
A. Hebecker, P. Henkenjohann and L.T. Witkowski, Flat monodromies and a moduli space size conjecture, JHEP 12 (2017) 033 [arXiv:1708.06761] [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].
R. Blumenhagen, D. Kläwer, L. Schlechter and F. Wolf, The refined swampland distance conjecture in Calabi-Yau moduli spaces, JHEP 06 (2018) 052 [arXiv:1803.04989] [INSPIRE].
E. Gonzalo, L.E. Ibáñez and Á.M. Uranga, Modular symmetries and the swampland conjectures, JHEP 05 (2019) 105 [arXiv:1812.06520] [INSPIRE].
G. Buratti, J. Calderón and A.M. Uranga, Transplanckian axion monodromy!?, JHEP 05 (2019) 176 [arXiv:1812.05016] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, A stringy test of the scalar weak gravity conjecture, Nucl. Phys. B 938 (2019) 321 [arXiv:1810.05169] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Tensionless strings and the weak gravity conjecture, JHEP 10 (2018) 164 [arXiv:1808.05958] [INSPIRE].
F. Marchesano and M. Wiesner, Instantons and infinite distances, JHEP 08 (2019) 088 [arXiv:1904.04848] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Emergent strings from infinite distance limits, arXiv:1910.01135 [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Emergent strings, duality and weak coupling limits for two-form fields, arXiv:1904.06344 [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].
A. Landete, F. Marchesano, G. Shiu and G. Zoccarato, Flux flattening in axion monodromy inflation, JHEP 06 (2017) 071 [arXiv:1703.09729] [INSPIRE].
A. Hebecker, P. Mangat, F. Rompineve and L.T. Witkowski, Tuning and backreaction in F-term axion monodromy inflation, Nucl. Phys. B 894 (2015) 456 [arXiv:1411.2032] [INSPIRE].
R. Blumenhagen, D. Herschmann and E. Plauschinn, The challenge of realizing F-term axion monodromy inflation in string theory, JHEP 01 (2015) 007 [arXiv:1409.7075] [INSPIRE].
M.J. Duff, J.T. Liu and R. Minasian, Eleven-dimensional origin of string-string duality: a one loop test, Nucl. Phys. B 452 (1995) 261 [hep-th/9506126] [INSPIRE].
S. Sethi, C. Vafa and E. Witten, Constraints on low dimensional string compactifications, Nucl. Phys. B 480 (1996) 213 [hep-th/9606122] [INSPIRE].
M. Berg, M. Haack and H. Samtleben, Calabi-Yau fourfolds with flux and supersymmetry breaking, JHEP 04 (2003) 046 [hep-th/0212255] [INSPIRE].
T.W. Grimm, The N = 1 effective action of F-theory compactifications, Nucl. Phys. B 845 (2011) 48 [arXiv:1008.4133] [INSPIRE].
K. Becker and M. Becker, M -theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [INSPIRE].
K. Dasgupta, G. Rajesh and S. Sethi, M -theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].
T.W. Grimm, T.G. Pugh and M. Weissenbacher, On M -theory fourfold vacua with higher curvature terms, Phys. Lett. B 743 (2015) 284 [arXiv:1408.5136] [INSPIRE].
T.W. Grimm, T.G. Pugh and M. Weissenbacher, The effective action of warped M-theory reductions with higher derivative terms. Part I, JHEP 01 (2016) 142 [arXiv:1412.5073] [INSPIRE].
T.W. Grimm, T.G. Pugh and M. Weissenbacher, The effective action of warped M-theory reductions with higher-derivative terms. Part II, JHEP 12 (2015) 117 [arXiv:1507.00343] [INSPIRE].
T.W. Grimm, K. Mayer and M. Weissenbacher, One-modulus Calabi-Yau fourfold reductions with higher-derivative terms, JHEP 04 (2018) 021 [arXiv:1712.07074] [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].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477] [hep-th/9906070] [INSPIRE].
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
T.W. Grimm, The effective action of type-II Calabi-Yau orientifolds, Fortsch. Phys. 53 (2005) 1179 [hep-th/0507153] [INSPIRE].
W. Schmid, Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973) 211.
M. Kashiwara, The asymptotic behavior of a variation of polarized Hodge structure, Publ. Res. Inst. Math. Sci. 21 (1985) 853.
G. Dvali, Three-form gauging of axion symmetries and gravity, hep-th/0507215 [INSPIRE].
N. Kaloper and L. Sorbo, A natural framework for chaotic inflation, Phys. Rev. Lett. 102 (2009) 121301 [arXiv:0811.1989] [INSPIRE].
N. Kaloper, A. Lawrence and L. Sorbo, An ignoble approach to large field inflation, JCAP 03 (2011) 023 [arXiv:1101.0026] [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].
T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, The D5-brane effective action and superpotential in N = 1 compactifications, Nucl. Phys. B 816 (2009) 139 [arXiv:0811.2996] [INSPIRE].
T.W. Grimm and D. Vieira Lopes, The N = 1 effective actions of D-branes in Type IIA and IIB orientifolds, Nucl. Phys. B 855 (2012) 639 [arXiv:1104.2328] [INSPIRE].
M. Kerstan and T. Weigand, The effective action of D6-branes in N = 1 type IIA orientifolds, JHEP 06 (2011) 105 [arXiv:1104.2329] [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. Farakos, S. Lanza, L. Martucci and D. Sorokin, Three-forms, supersymmetry and string compactifications, Phys. Part. Nucl. 49 (2018) 823 [arXiv:1712.09366] [INSPIRE].
I. Bandos et al., Three-forms, dualities and membranes in four-dimensional supergravity, JHEP 07 (2018) 028 [arXiv:1803.01405] [INSPIRE].
D. Escobar, F. Marchesano and W. Staessens, Type IIA flux vacua and α′ -corrections, JHEP 06 (2019) 129 [arXiv:1812.08735] [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].
F. Marchesano and J. Quirant, A landscape of AdS flux vacua, JHEP 12 (2019) 110 [arXiv:1908.11386] [INSPIRE].
E. García-Valdecasas and A. Uranga, On the 3-form formulation of axion potentials from D-brane instantons, JHEP 02 (2017) 087 [arXiv:1605.08092] [INSPIRE].
T.W. Grimm, F. Ruehle and D. van de Heisteeg, Classifying Calabi-Yau threefolds using infinite distance limits, arXiv:1910.02963 [INSPIRE].
R. Donagi, S. Katz and M. Wijnholt, Weak coupling, degeneration and log Calabi-Yau spaces, arXiv:1212.0553 [INSPIRE].
A. Clingher, R. Donagi and M. Wijnholt, The Sen Limit, Adv. Theor. Math. Phys. 18 (2014) 613 [arXiv:1212.4505] [INSPIRE].
S.S. Haque, G. Shiu, B. Underwood and T. Van Riet, Minimal simple de Sitter solutions, Phys. Rev. D 79 (2009) 086005 [arXiv:0810.5328] [INSPIRE].
B. de Carlos, A. Guarino and J.M. Moreno, Flux moduli stabilisation, supergravity algebras and no-go theorems, JHEP 01 (2010) 012 [arXiv:0907.5580] [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].
D. Andriot and J. Blåbäck, Refining the boundaries of the classical de Sitter landscape, JHEP 03 (2017) 102 [Erratum ibid. 03 (2018) 083] [arXiv:1609.00385] [INSPIRE].
D. Andriot, On classical de Sitter and Minkowski solutions with intersecting branes, JHEP 03 (2018) 054 [arXiv:1710.08886] [INSPIRE].
D. Andriot, New constraints on classical de Sitter: flirting with the swampland, Fortsch. Phys. 67 (2019) 1800103 [arXiv:1807.09698] [INSPIRE].
J. Blåbäck, U. Danielsson and G. Dibitetto, A new light on the darkest corner of the landscape, arXiv:1810.11365 [INSPIRE].
P. Shukla, T -dualizing the de-Sitter no-go scenarios, arXiv:1909.08630 [INSPIRE].
L.F. Alday and E. Perlmutter, Growing extra dimensions in AdS/CFT, JHEP 08 (2019) 084 [arXiv:1906.01477] [INSPIRE].
D. Lüst, E. Palti and C. Vafa, AdS and the Swampland, Phys. Lett. B 797 (2019) 134867 [arXiv:1906.05225].
P.G. Camara, 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].
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].
E. Silverstein and A. Westphal, Monodromy in the CMB: gravity waves and string inflation, Phys. Rev. D 78 (2008) 106003 [arXiv:0803.3085] [INSPIRE].
L. McAllister, E. Silverstein and A. Westphal, Gravity waves and linear inflation from axion monodromy, Phys. Rev. D 82 (2010) 046003 [arXiv:0808.0706] [INSPIRE].
L. McAllister, E. Silverstein, A. Westphal and T. Wrase, The powers of monodromy, JHEP 09 (2014) 123 [arXiv:1405.3652] [INSPIRE].
F. Marchesano, G. Shiu and A.M. Uranga, F-term axion monodromy inflation, JHEP 09 (2014) 184 [arXiv:1404.3040] [INSPIRE].
A. Hebecker, S.C. Kraus and L.T. Witkowski, D7-brane chaotic inflation, Phys. Lett. B 737 (2014) 16 [arXiv:1404.3711] [INSPIRE].
R. Blumenhagen and E. Plauschinn, Towards universal axion inflation and reheating in string theory, Phys. Lett. B 736 (2014) 482 [arXiv:1404.3542] [INSPIRE].
L.E. Ibáñez and I. Valenzuela, The inflaton as an MSSM Higgs and open string modulus monodromy inflation, Phys. Lett. B 736 (2014) 226 [arXiv:1404.5235] [INSPIRE].
A. Bedroya and C. Vafa, Trans-Planckian censorship and the swampland, arXiv:1909.11063 [INSPIRE].
P. Draper and S. Farkas, Transplanckian censorship and the local swampland distance conjecture, JHEP 01 (2020) 133 [arXiv:1910.04804] [INSPIRE].
M. Kim and L. McAllister, Monodromy charge in D7-brane inflation, arXiv:1812.03532 [INSPIRE].
L.E. Ibáñez, F. Marchesano and I. Valenzuela, Higgs-otic inflation and string theory, JHEP 01 (2015) 128 [arXiv:1411.5380] [INSPIRE].
M. Scalisi and I. Valenzuela, Swampland distance conjecture, inflation and α-attractors, JHEP 08 (2019) 160 [arXiv:1812.07558] [INSPIRE].
P. Deligne, Structures de Hodge mixtes réelles, in Motives, U. Jannsen et al. eds., Proceedings of Symposia in Pure Mathematics volume 55, American Mathematical Society, Providence U.S.A. (1994).
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
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: 1910.09549
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Grimm, T.W., Li, C. & Valenzuela, I. Asymptotic flux compactifications and the swampland. J. High Energ. Phys. 2020, 9 (2020). https://doi.org/10.1007/JHEP06(2020)009
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2020)009