×

Moduli stabilisation for chiral global models. (English) Zbl 1309.81208

Summary: We combine moduli stabilisation and (chiral) model building in a fully con-sistent global set-up in Type IIB/F-theory. We consider compactifications on Calabi-Yau orientifolds which admit an explicit description in terms of toric geometry. We build globally consistent compactifications with tadpole and Freed-Witten anomaly cancellation by choosing appropriate brane set-ups and world-volume fluxes which also give rise to \(\operatorname{SU}(5)\) or MSSM-like chiral models. We fix all the Kähler moduli within the Kähler cone and the regime of validity of the 4D effective field theory. This is achieved in a way compatible with the local presence of chirality. The hidden sector generating the non-perturbative effects is placed on a del Pezzo divisor that does not have any chiral intersection with any other brane. In general, the vanishing D-term condition implies the shrinking of the rigid divisor supporting the visible sector. However, we avoid this problem by generating \(r < n\) D-term conditions on a set of \(n\) intersecting divisors. The remaining (\(n - r\)) flat directions are fixed by perturbative corrections to the Kähler potential. We illustrate our general claims in an explicit example. We consider a K3-fibred Calabi-Yau with four Kähler moduli, that is a hypersurface in a toric ambient space and admits a ’simple’ F-theory up-lift. We present explicit choices of brane set-ups and fluxes which lead to three different phenomenological scenarios: the first with GUT-scale strings and TeV-scale SUSY by fine-tuning the background fluxes; the second with an exponentially large value of the volume and TeV-scale SUSY without fine-tuning the background fluxes; and the third with a very anisotropic configuration that leads to TeV-scale strings and two micron-sized extra dimensions. The \(K3\) fibration structure of the Calabi-Yau three-fold is also particularly suitable for cosmological purposes.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
81T50 Anomalies in quantum field theory
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
14D06 Fibrations, degenerations in algebraic geometry

Software:

PALP

References:

[1] J. Polchinski, Dirichlet Branes and Ramond-Ramond charges, Phys. Rev. Lett.75 (1995) 4724 [hep-th/9510017] [INSPIRE]. · Zbl 1020.81797 · doi:10.1103/PhysRevLett.75.4724
[2] B. de Wit, D. Smit and N. Hari Dass, Residual Supersymmetry of Compactified D = 10 Supergravity, Nucl. Phys.B 283 (1987) 165 [INSPIRE]. · doi:10.1016/0550-3213(87)90267-7
[3] 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]. · Zbl 0984.83052
[4] S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev.D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
[5] K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G - flux, JHEP08 (1999) 023 [hep-th/9908088] [INSPIRE]. · Zbl 1060.81575 · doi:10.1088/1126-6708/1999/08/023
[6] M. Graña, Flux compactifications in string theory: a Comprehensive review, Phys. Rept.423 (2006) 91 [hep-th/0509003] [INSPIRE]. · doi:10.1016/j.physrep.2005.10.008
[7] M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys.79 (2007) 733 [hep-th/0610102] [INSPIRE]. · Zbl 1205.81011 · doi:10.1103/RevModPhys.79.733
[8] 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]. · doi:10.1016/j.physrep.2007.04.003
[9] F. Denef, Les Houches Lectures on Constructing String Vacua, arXiv:0803.1194 [INSPIRE].
[10] 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]. · Zbl 1244.83036
[11] V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP03 (2005) 007 [hep-th/0502058] [INSPIRE]. · doi:10.1088/1126-6708/2005/03/007
[12] M. Berg, M. Haack and B. Körs, On volume stabilization by quantum corrections, Phys. Rev. Lett.96 (2006) 021601 [hep-th/0508171] [INSPIRE]. · doi:10.1103/PhysRevLett.96.021601
[13] J. Cascales, M. Garcia del Moral, F. Quevedo and A. Uranga, Realistic D-brane models on warped throats: Fluxes, hierarchies and moduli stabilization, JHEP02 (2004) 031 [hep-th/0312051] [INSPIRE]. · doi:10.1088/1126-6708/2004/02/031
[14] F. Marchesano and G. Shiu, Building MSSM flux vacua, JHEP11 (2004) 041 [hep-th/0409132] [INSPIRE]. · doi:10.1088/1126-6708/2004/11/041
[15] M. Cvetič, T. Li and T. Liu, Standard-like models as type IIB flux vacua, Phys. Rev.D 71 (2005) 106008 [hep-th/0501041] [INSPIRE].
[16] B.S. Acharya, F. Benini and R. Valandro, Warped models in string theory, hep-th/0612192 [INSPIRE]. · Zbl 1119.81361
[17] R. Donagi and M. Wijnholt, Model Building with F-theory, arXiv:0802.2969. 49p, 5 figs, Latex [INSPIRE]. · Zbl 1260.81194
[18] C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory - I, JHEP01 (2009) 058 [arXiv:0802.3391] [INSPIRE]. · Zbl 1243.81142 · doi:10.1088/1126-6708/2009/01/058
[19] C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory - II: Experimental Predictions, JHEP01 (2009) 059 [arXiv:0806.0102] [INSPIRE]. · Zbl 1243.81141 · doi:10.1088/1126-6708/2009/01/059
[20] H. Hayashi, R. Tatar, Y. Toda, T. Watari and M. Yamazaki, New Aspects of Heterotic-F Theory Duality, Nucl. Phys.B 806 (2009) 224 [arXiv:0805.1057] [INSPIRE]. · Zbl 1192.81270 · doi:10.1016/j.nuclphysb.2008.07.031
[21] J.P. Conlon, A. Maharana and F. Quevedo, Towards Realistic String Vacua, JHEP05 (2009) 109 [arXiv:0810.5660] [INSPIRE]. · doi:10.1088/1126-6708/2009/05/109
[22] J. Marsano, N. Saulina and S. Schäfer-Nameki, Monodromies, Fluxes and Compact Three-Generation F-theory GUTs, JHEP08 (2009) 046 [arXiv:0906.4672] [INSPIRE]. · doi:10.1088/1126-6708/2009/08/046
[23] J.P. Conlon and E. Palti, Aspects of Flavour and Supersymmetry in F-theory GUTs, JHEP01 (2010) 029 [arXiv:0910.2413] [INSPIRE]. · Zbl 1269.81117 · doi:10.1007/JHEP01(2010)029
[24] P.G. Camara, E. Dudas and E. Palti, Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs, JHEP12 (2011) 112 [arXiv:1110.2206] [INSPIRE]. · Zbl 1306.81397 · doi:10.1007/JHEP12(2011)112
[25] R. Blumenhagen, V. Braun, T.W. Grimm and T. Weigand, GUTs in Type IIB Orientifold Compactifications, Nucl. Phys.B 815 (2009) 1 [arXiv:0811.2936] [INSPIRE]. · Zbl 1194.81288 · doi:10.1016/j.nuclphysb.2009.02.011
[26] A. Collinucci, M. Kreuzer, C. Mayrhofer and N.-O. Walliser, Four-modulus ’Swiss Cheese’ chiral models, JHEP07 (2009) 074 [arXiv:0811.4599] [INSPIRE]. · doi:10.1088/1126-6708/2009/07/074
[27] R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, Global F-theory GUTs, Nucl. Phys.B 829 (2010) 325 [arXiv:0908.1784] [INSPIRE]. · Zbl 1203.81188 · doi:10.1016/j.nuclphysb.2009.12.013
[28] J. Marsano, N. Saulina and S. Schäfer-Nameki, Compact F-theory GUTs with U(1) (PQ), JHEP04 (2010) 095 [arXiv:0912.0272] [INSPIRE]. · Zbl 1272.81163 · doi:10.1007/JHEP04(2010)095
[29] T.W. Grimm, S. Krause and T. Weigand, F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds, JHEP07 (2010) 037 [arXiv:0912.3524] [INSPIRE]. · Zbl 1290.81211 · doi:10.1007/JHEP07(2010)037
[30] M. Cvetič, I. Garcia-Etxebarria and J. Halverson, Global F-theory Models: Instantons and Gauge Dynamics, JHEP01 (2011) 073 [arXiv:1003.5337] [INSPIRE]. · Zbl 1214.81149 · doi:10.1007/JHEP01(2011)073
[31] C.-M. Chen, J. Knapp, M. Kreuzer and C. Mayrhofer, Global SO(10) F-theory GUTs, JHEP10 (2010) 057 [arXiv:1005.5735] [INSPIRE]. · Zbl 1291.81300
[32] C. Mayrhofer, Compactifications of Type IIB String Theory and F-Theory Models by Means of Toric Geometry, Ph.D. thesis, Vienna University of Technology, Vienna (2010).
[33] R. Blumenhagen, S. Moster and E. Plauschinn, Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds, JHEP01 (2008) 058 [arXiv:0711.3389] [INSPIRE]. · doi:10.1088/1126-6708/2008/01/058
[34] M. Cicoli, M. Kreuzer and C. Mayrhofer, Toric K3-Fibred Calabi-Yau Manifolds with del Pezzo Divisors for String Compactifications, JHEP02 (2012) 002 [arXiv:1107.0383] [INSPIRE]. · Zbl 1309.81149 · doi:10.1007/JHEP02(2012)002
[35] M. Cicoli, C. Burgess and F. Quevedo, Anisotropic Modulus Stabilisation: Strings at LHC Scales with Micron-sized Extra Dimensions, JHEP10 (2011) 119 [arXiv:1105.2107] [INSPIRE]. · Zbl 1303.81154 · doi:10.1007/JHEP10(2011)119
[36] M. Cicoli, C. Burgess and F. Quevedo, Fibre Inflation: Observable Gravity Waves from IIB String Compactifications, JCAP03 (2009) 013 [arXiv:0808.0691] [INSPIRE]. · doi:10.1088/1475-7516/2009/03/013
[37] R. Minasian and G.W. Moore, K theory and Ramond-Ramond charge, JHEP11 (1997) 002 [hep-th/9710230] [INSPIRE]. · Zbl 0949.81511 · doi:10.1088/1126-6708/1997/11/002
[38] D.S. Freed and E. Witten, Anomalies in string theory with D-branes, Asian J. Math3 (1999) 819 [hep-th/9907189] [INSPIRE]. · Zbl 1028.81052
[39] 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]. · Zbl 0984.81143
[40] H. Jockers and J. Louis, D-terms and F-terms from D7-brane fluxes, Nucl. Phys.B 718 (2005) 203 [hep-th/0502059] [INSPIRE]. · Zbl 1207.81126 · doi:10.1016/j.nuclphysb.2005.04.011
[41] M. Haack, D. Krefl, D. Lüst, A. Van Proeyen and M. Zagermann, Gaugino Condensates and D-terms from D7-branes, JHEP01 (2007) 078 [hep-th/0609211] [INSPIRE]. · doi:10.1088/1126-6708/2007/01/078
[42] M. Dine, N. Seiberg and E. Witten, Fayet-Iliopoulos Terms in String Theory, Nucl. Phys.B 289 (1987) 589 [INSPIRE]. · doi:10.1016/0550-3213(87)90395-6
[43] M. Cicoli, J.P. Conlon and F. Quevedo, General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation, JHEP10 (2008) 105 [arXiv:0805.1029] [INSPIRE]. · Zbl 1245.81155 · doi:10.1088/1126-6708/2008/10/105
[44] R. Blumenhagen, J. Conlon, S. Krippendorf, S. Moster and F. Quevedo, SUSY Breaking in Local String/F-Theory Models, JHEP09 (2009) 007 [arXiv:0906.3297] [INSPIRE]. · doi:10.1088/1126-6708/2009/09/007
[45] K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and alpha-prime corrections to flux induced potentials, JHEP06 (2002) 060 [hep-th/0204254] [INSPIRE]. · doi:10.1088/1126-6708/2002/06/060
[46] M. Berg, M. Haack and B. Körs, String loop corrections to Kähler potentials in orientifolds, JHEP11 (2005) 030 [hep-th/0508043] [INSPIRE]. · doi:10.1088/1126-6708/2005/11/030
[47] M. Berg, M. Haack and E. Pajer, Jumping Through Loops: On Soft Terms from Large Volume Compactifications, JHEP09 (2007) 031 [arXiv:0704.0737] [INSPIRE]. · doi:10.1088/1126-6708/2007/09/031
[48] M. Cicoli, J.P. Conlon and F. Quevedo, Systematics of String Loop Corrections in Type IIB Calabi-Yau Flux Compactifications, JHEP01 (2008) 052 [arXiv:0708.1873] [INSPIRE]. · doi:10.1088/1126-6708/2008/01/052
[49] T.W. Grimm, M. Kerstan, E. Palti and T. Weigand, On Fluxed Instantons and Moduli Stabilisation in IIB Orientifolds and F-theory, Phys. Rev.D 84 (2011) 066001 [arXiv:1105.3193] [INSPIRE].
[50] M. Cicoli and A. Mazumdar, Reheating for Closed String Inflation, JCAP09 (2010) 025 [arXiv:1005.5076] [INSPIRE]. · doi:10.1088/1475-7516/2010/09/025
[51] K.A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP(N(c)) gauge theories, Phys. Lett.B 353 (1995) 471 [hep-th/9505006] [INSPIRE].
[52] K. Bobkov, V. Braun, P. Kumar and S. Raby, Stabilizing All Kähler Moduli in Type IIB Orientifolds, JHEP12 (2010) 056 [arXiv:1003.1982] [INSPIRE]. · Zbl 1294.81166 · doi:10.1007/JHEP12(2010)056
[53] M. Kreuzer and H. Skarke, PALP: A Package for analyzing lattice polytopes with applications to toric geometry, Comput. Phys. Commun.157 (2004) 87 [math/0204356] [INSPIRE]. · Zbl 1196.14007 · doi:10.1016/S0010-4655(03)00491-0
[54] A.P. Braun and N.-O. Walliser, A New offspring of PALP, arXiv:1106.4529 [INSPIRE].
[55] L. Martucci, D-branes on general N = 1 backgrounds: Superpotentials and D-terms, JHEP06 (2006) 033 [hep-th/0602129] [INSPIRE]. · doi:10.1088/1126-6708/2006/06/033
[56] D. Lüst, P. Mayr, S. Reffert and S. Stieberger, F-theory flux, destabilization of orientifolds and soft terms on D7-branes, Nucl. Phys.B 732 (2006) 243 [hep-th/0501139] [INSPIRE]. · Zbl 1192.81278 · doi:10.1016/j.nuclphysb.2005.09.011
[57] A.P. Braun, A. Hebecker, C. Lüdeling and R. Valandro, Fixing D7 Brane Positions by F-theory Fluxes, Nucl. Phys.B 815 (2009) 256 [arXiv:0811.2416] [INSPIRE]. · Zbl 1194.83094 · doi:10.1016/j.nuclphysb.2009.02.025
[58] V. Batyrev and M. Kreuzer, Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions, arXiv:0802.3376 [INSPIRE]. · Zbl 1242.14037
[59] T.C.T. Wall, Classification Problems in Differential Topology. V; On Certain 6-Manifolds, Invent. math.1 (1966) 355. · Zbl 0149.20601 · doi:10.1007/BF01389738
[60] A. Collinucci, F. Denef and M. Esole, D-brane Deconstructions in IIB Orientifolds, JHEP02 (2009) 005 [arXiv:0805.1573] [INSPIRE]. · Zbl 1245.81156 · doi:10.1088/1126-6708/2009/02/005
[61] A. Braun, A. Hebecker and H. Triendl, D7-Brane Motion from M-theory Cycles and Obstructions in the Weak Coupling Limit, Nucl. Phys.B 800 (2008) 298 [arXiv:0801.2163] [INSPIRE]. · Zbl 1309.81203 · doi:10.1016/j.nuclphysb.2008.03.021
[62] E. Witten, D-branes and k-theory, JHEP12 (1998) 019 [hep-th/9810188] [INSPIRE]. · Zbl 0959.81070 · doi:10.1088/1126-6708/1998/12/019
[63] G.W. Moore and E. Witten, Selfduality, Ramond-Ramond fields and k-theory, JHEP05 (2000) 032 [hep-th/9912279] [INSPIRE]. · Zbl 0990.81626 · doi:10.1088/1126-6708/2000/05/032
[64] A.M. Uranga, D-brane probes, RR tadpole cancellation and k-theory charge, Nucl. Phys.B 598 (2001) 225 [hep-th/0011048] [INSPIRE]. · Zbl 1046.81543 · doi:10.1016/S0550-3213(00)00787-2
[65] M. Goodsell, J. Jaeckel, J. Redondo and A. Ringwald, Naturally Light Hidden Photons in LARGE Volume String Compactifications, JHEP11 (2009) 027 [arXiv:0909.0515] [INSPIRE]. · doi:10.1088/1126-6708/2009/11/027
[66] M. Cicoli, M. Goodsell, J. Jaeckel and A. Ringwald, Testing String Vacua in the Lab: From a Hidden CMB to Dark Forces in Flux Compactifications, JHEP07 (2011) 114 [arXiv:1103.3705] [INSPIRE]. · Zbl 1298.81257 · doi:10.1007/JHEP07(2011)114
[67] C. Burgess, R. Kallosh and F. Quevedo, de Sitter string vacua from supersymmetric D terms, JHEP10 (2003) 056 [hep-th/0309187] [INSPIRE].
[68] A. Saltman and E. Silverstein, The Scaling of the no scale potential and de Sitter model building, JHEP11 (2004) 066 [hep-th/0402135] [INSPIRE]. · doi:10.1088/1126-6708/2004/11/066
[69] H. Abe, T. Higaki, T. Kobayashi and Y. Omura, Moduli stabilization, F-term uplifting and soft supersymmetry breaking terms, Phys. Rev.D 75 (2007) 025019 [hep-th/0611024] [INSPIRE].
[70] J.P. Conlon, S.S. AbdusSalam, F. Quevedo and K. Suruliz, Soft SUSY Breaking Terms for Chiral Matter in IIB String Compactifications, JHEP01 (2007) 032 [hep-th/0610129] [INSPIRE]. · doi:10.1088/1126-6708/2007/01/032
[71] A. Collinucci, New F-theory lifts, JHEP08 (2009) 076 [arXiv:0812.0175] [INSPIRE]. · Zbl 1272.81147 · doi:10.1088/1126-6708/2009/08/076
[72] A. Collinucci, New F-theory lifts. II. Permutation orientifolds and enhanced singularities, JHEP04 (2010) 076 [arXiv:0906.0003] [INSPIRE]. · Zbl 1272.81147 · doi:10.1007/JHEP04(2010)076
[73] R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, F-theory uplifts and GUTs, JHEP09 (2009) 053 [arXiv:0906.0013] [INSPIRE]. · doi:10.1088/1126-6708/2009/09/053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.