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.
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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].
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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
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DOI: https://doi.org/10.1007/JHEP04(2020)001