Abstract
We examine the vacuum structure of 4D effective theories of moduli fields in spacetime compactifications with quantized background fluxes. Imposing the no-scale structure for the volume deformations, we numerically investigate the distributions of flux vacua of the effective potential in complex structure moduli and axio-dilaton directions for two explicit examples in Type IIB string theory and F-theory compactifications. It turns out that distributions of non-supersymmetric flux vacua exhibit a non-increasing functional behavior of several on-shell quantities with respect to the string coupling. We point out that this phenomena can be deeply connected with a previously-reported possible correspondence between the flux vacua in moduli stabilization problem and the attractor mechanism in supergravity, and our explicit demonstration implies that such a correspondence generically exist even in the framework of F-theory. In particular, we confirm that the solutions of the effective potential we explicitly evaluated in Type IIB and F-theory flux compactifications indeed satisfy the generalized form of the attractor equations simultaneously.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [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].
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].
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [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].
J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].
A. Saltman and E. Silverstein, The scaling of the no scale potential and de Sitter model building, JHEP 11 (2004) 066 [hep-th/0402135] [INSPIRE].
D. Gallego, M.C.D. Marsh, B. Vercnocke and T. Wrase, A new class of de Sitter vacua in type IIB large volume compactifications, JHEP 10 (2017) 193 [arXiv:1707.01095] [INSPIRE].
J. Bl°ab¨ack, U.H. Danielsson, G. Dibitetto and S.C. Vargas, Universal dS vacua in STU-models, JHEP 10 (2015) 069 [arXiv:1505.04283] [INSPIRE].
R. Kallosh, New attractors, JHEP 12 (2005) 022 [hep-th/0510024] [INSPIRE].
R. Kallosh, Flux vacua as supersymmetric attractors, hep-th/0509112 [INSPIRE].
R. Kallosh, N. Sivanandam and M. Soroush, The non-BPS black hole attractor equation, JHEP 03 (2006) 060 [hep-th/0602005] [INSPIRE].
M. Alishahiha and H. Ebrahim, New attractor, entropy function and black hole partition function, JHEP 11 (2006) 017 [hep-th/0605279] [INSPIRE].
S. Bellucci, S. Ferrara, R. Kallosh and A. Marrani, Extremal black hole and flux vacua attractors, Lect. Notes Phys. 755 (2008) 115 [arXiv:0711.4547] [INSPIRE].
F. Larsen and R. O’Connell, Flux attractors and generating functions, JHEP 07 (2009) 049 [arXiv:0905.2130] [INSPIRE].
S. Kachru, M.B. Schulz and S. Trivedi, Moduli stabilization from fluxes in a simple IIB orientifold, JHEP 10 (2003) 007 [hep-th/0201028] [INSPIRE].
A.R. Frey and J. Polchinski, N = 3 warped compactifications, Phys. Rev. D 65 (2002) 126009 [hep-th/0201029] [INSPIRE].
R. D’Auria, S. Ferrara and S. Vaula, N = 4 gauged supergravity and a IIB orientifold with fluxes, New J. Phys. 4 (2002) 71 [hep-th/0206241] [INSPIRE].
A.R. Frey and A. Mazumdar, Three form induced potentials, dilaton stabilization and running moduli, Phys. Rev. D 67 (2003) 046006 [hep-th/0210254] [INSPIRE].
M. Dine and N. Seiberg, Is the superstring weakly coupled?, Phys. Lett. B 162 (1985) 299.
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].
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].
Y. Honma and H. Otsuka, On the flux vacua in F-theory compactifications, Phys. Lett. B 774 (2017) 225 [arXiv:1706.09417] [INSPIRE].
K. Becker and M. Becker, M theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [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. Haack and J. Louis, M theory compactified on Calabi-Yau fourfolds with background flux, Phys. Lett. B 507 (2001) 296 [hep-th/0103068] [INSPIRE].
F. Denef, Les Houches Lectures on Constructing String Vacua, Les Houches 87 (2008) 483 [arXiv:0803.1194] [INSPIRE].
M. Alim et al., Hints for off-shell mirror symmetry in type-II/F-theory compactifications, Nucl. Phys. B 841 (2010) 303 [arXiv:0909.1842] [INSPIRE].
T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, Computing brane and flux superpotentials in F-theory compactifications, JHEP 04 (2010) 015 [arXiv:0909.2025] [INSPIRE].
H. Jockers, P. Mayr and J. Walcher, On N = 1 4d effective couplings for F-theory and heterotic vacua, Adv. Theor. Math. Phys. 14 (2010) 1433 [arXiv:0912.3265] [INSPIRE].
T.W. Grimm, A. Klemm and D. Klevers, Five-brane superpotentials, blow-up geometries and SU(3) structure manifolds, JHEP 05 (2011) 113 [arXiv:1011.6375] [INSPIRE].
Y. Honma and M. Manabe, Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces, JHEP 03 (2016) 160 [arXiv:1507.08342] [INSPIRE].
Y. Honma and M. Manabe, Exact K¨ahler potential for Calabi-Yau fourfolds, JHEP 05 (2013) 102 [arXiv:1302.3760] [INSPIRE].
T.W. Grimm, R. Savelli and M. Weissenbacher, On α! corrections in N = 1 F-theory compactifications, Phys. Lett. B 725 (2013) 431 [arXiv:1303.3317] [INSPIRE].
T.W. Grimm, J. Keitel, R. Savelli and M. Weissenbacher, From M-theory higher curvature terms to α! corrections in F-theory, Nucl. Phys. B 903 (2016) 325 [arXiv:1312.1376] [INSPIRE].
R. Minasian, T.G. Pugh and R. Savelli, F-theory at order α!3 , JHEP 10 (2015) 050 [arXiv:1506.06756] [INSPIRE].
M. Weissenbacher, F-theory vacua and α′ -corrections, arXiv:1901.04758 [INSPIRE].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) R5412 [hep-th/9508072] [INSPIRE].
S. Ferrara, K. Hayakawa and A. Marrani, Lectures on attractors and black holes, Fortsch. Phys. 56 (2008) 993 [arXiv:0805.2498] [INSPIRE].
G.W. Moore, Strings and arithmetic, hep-th/0401049 [INSPIRE].
F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP 05 (2004) 072 [hep-th/0404116] [INSPIRE].
R. Blumenhagen, D. Lüst and T.R. Taylor, Moduli stabilization in chiral type IIB orientifold models with fluxes, Nucl. Phys. B 663 (2003) 319 [hep-th/0303016] [INSPIRE].
J.F.G. Cascales and A.M. Uranga, Chiral 4d string vacua with D-branes and NS-NS and RR fluxes, JHEP 05 (2003) 011 [hep-th/0303024] [INSPIRE].
T.W. Grimm, C. Li and I. Valenzuela, Asymptotic flux compactifications and the swampland, arXiv:1910.09549 [INSPIRE].
G. Hulsey, S. Kachru, S. Yang and M. Zimet, Distributions of extremal black holes in Calabi-Yau compactifications, arXiv:1901.10614 [INSPIRE].
K. Dasgupta, R. Gwyn, E. McDonough, M. Mia and R. Tatar, De Sitter vacua in type IIB string theory: classical solutions and quantum corrections, JHEP 07 (2014) 054 [arXiv:1402.5112] [INSPIRE].
A. Kehagias, D. Lüst and S. Lüst, Swampland, gradient flow and infinite distance, arXiv:1910.00453 [INSPIRE].
I. Bena, E. Dudas, M. Graña and S. Lüst, Uplifting runaways, Fortsch. Phys. 67 (2019) 1800100 [arXiv:1809.06861] [INSPIRE].
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
ArXiv ePrint: 1910.10725
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
Honma, Y., Otsuka, H. F-theory flux vacua and attractor equations. J. High Energ. Phys. 2020, 1 (2020). https://doi.org/10.1007/JHEP04(2020)001
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2020)001