Abstract
F-theory compactified on a Calabi-Yau fourfold naturally describes non- Abelian gauge symmetries through the singularity structure of the elliptic fibration. In contrast Abelian symmetries are more difficult to study because of their inherently global nature. We argue that in general F-theory compactifications there are massive Abelian symmetries, such as the uplift of the Abelian part of the U(N) gauge group on D7-branes, that arise from non-Kähler resolutions of the dual M-theory setup. The four-dimensional F-theory vacuum with vanishing expectation values for the gauge fields corresponds to the Calabi-Yau limit. We propose that fluxes that are turned on along these U(1)s are uplifted to non-harmonic four-form fluxes. We derive the effective four-dimensional gauged su- pergravity resulting from F-theory compactifications in the presence of the Abelian gauge factors including the effects of possible fluxes on the gauging, tadpoles and matter spectrum.
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References
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
F. Denef, Les Houches Lectures on Constructing String Vacua, arXiv:0803.1194 [INSPIRE].
T. Weigand, Lectures on F-theory compactifications and model building, Class. Quant. Grav. 27 (2010) 214004 [arXiv:1009.3497] [INSPIRE].
R. Donagi and M. Wijnholt, Model Building with F-theory, arXiv:0802.2969 [INSPIRE].
C. Beasley, J. J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory - I, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory - II: Experimental Predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [INSPIRE].
R. Donagi and M. Wijnholt, Breaking GUT Groups in F-theory, arXiv:0808.2223 [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 1, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2., Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
M. Bershadsky, K.A. Intriligator, S. Kachru, D.R. Morrison, V. Sadov and C. Vafa, Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481 (1996) 215 [hep-th/9605200] [INSPIRE].
S.H. Katz and C. Vafa, Matter from geometry, Nucl. Phys. B 497 (1997) 146 [hep-th/9606086] [INSPIRE].
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].
J. Marsano, N. Saulina and S. Schäfer-Nameki, F-theory Compactifications for Supersymmetric GUTs, JHEP 08 (2009) 030 [arXiv:0904.3932] [INSPIRE].
R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, Global F-theory GUTs, Nucl. Phys. B 829 (2010) 325 [arXiv:0908.1784] [INSPIRE].
T.W. Grimm, S. Krause and T. Weigand, F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds, JHEP 07 (2010) 037 [arXiv:0912.3524] [INSPIRE].
P. Candelas and A. Font, Duality between the webs of heterotic and type-II vacua, Nucl. Phys. B 511 (1998) 295 [hep-th/9603170] [INSPIRE].
P. Candelas, E. Perevalov and G. Rajesh, Toric geometry and enhanced gauge symmetry of F-theory/heterotic vacua, Nucl. Phys. B 507 (1997) 445 [hep-th/9704097] [INSPIRE].
C.-M. Chen, J. Knapp, M. Kreuzer and C. Mayrhofer, Global SO(10) F-theory GUTs, JHEP 10 (2010) 057 [arXiv:1005.5735] [INSPIRE].
J. Knapp, M. Kreuzer, C. Mayrhofer and N.-O. Walliser, Toric Construction of Global F-theory GUTs, JHEP 03 (2011) 138 [arXiv:1101.4908] [INSPIRE].
D.R. Morrison and W. Taylor, Matter and singularities, arXiv:1106.3563 [INSPIRE].
S. Katz, D.R. Morrison, S. Schäfer-Nameki and J. Sully, Tate’s algorithm and F-theory, JHEP 08 (2011) 094 [arXiv:1106.3854] [INSPIRE].
M. Esole and S.-T. Yau, Small resolutions of SU(5)-models in F-theory, arXiv:1107.0733 [INSPIRE].
T.W. Grimm and T. Weigand, On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs, Phys. Rev. D 82 (2010) 086009 [arXiv:1006.0226] [INSPIRE].
H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, More on Dimension-4 Proton Decay Problem in F-theory - Spectral Surface, Discriminant Locus and Monodromy, Nucl. Phys. B 840 (2010) 304 [arXiv:1004.3870] [INSPIRE].
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].
H. Hayashi, T. Kawano, R. Tatar and T. Watari, Codimension-3 Singularities and Yukawa Couplings in F-theory, Nucl. Phys. B 823 (2009) 47 [arXiv:0901.4941] [INSPIRE].
R. Donagi and M. Wijnholt, Higgs Bundles and UV Completion in F-theory, arXiv:0904.1218 [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, A Note on G-fluxes for F-theory Model Building, JHEP 11 (2010) 088 [arXiv:1006.0483] [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, On G-flux, M5 instantons and U(1)s in F-theory, arXiv:1107.1718 [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].
F. Marchesano, Progress in D-brane model building, Fortsch. Phys. 55 (2007) 491 [hep-th/0702094] [INSPIRE].
M. Cvetič and J. Halverson, TASI Lectures: Particle Physics from Perturbative and Non-perturbative Effects in D-braneworlds, arXiv:1101.2907 [INSPIRE].
L. Ibáñez and A. Uranga, String Theory and Particle Physics - An Introduction to String Phenomenology, Cambridge University Press, Cambridge U.K. (2012).
R. Blumenhagen, M. Cvetič and T. Weigand, Spacetime instanton corrections in 4D string vacua: The Seesaw mechanism for D-brane models, Nucl. Phys. B 771 (2007) 113 [hep-th/0609191] [INSPIRE].
L. Ibáñez and A. Uranga, Neutrino Majorana Masses from String Theory Instanton Effects, JHEP 03 (2007) 052 [hep-th/0609213] [INSPIRE].
B. Florea, S. Kachru, J. McGreevy and N. Saulina, Stringy Instantons and Quiver Gauge Theories, JHEP 05 (2007) 024 [hep-th/0610003] [INSPIRE].
R. Blumenhagen, M. Cvetič, S. Kachru and T. Weigand, D-Brane Instantons in Type II Orientifolds, Ann. Rev. Nucl. Part. Sci. 59 (2009) 269 [arXiv:0902.3251] [INSPIRE].
R. Blumenhagen, S. Moster and E. Plauschinn, Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds, JHEP 01 (2008) 058 [arXiv:0711.3389] [INSPIRE].
R. Blumenhagen, J. Conlon, S. Krippendorf, S. Moster and F. Quevedo, SUSY Breaking in Local String/F-Theory Models, JHEP 09 (2009) 007 [arXiv:0906.3297] [INSPIRE].
S. Abel, M. Goodsell, J. Jaeckel, V. Khoze and A. Ringwald, Kinetic Mixing of the Photon with Hidden U(1)s in String Phenomenology, JHEP 07 (2008) 124 [arXiv:0803.1449] [INSPIRE].
C. Burgess, J. Conlon, L.-Y. Hung, C. Kom, A. Maharana and F. Quevedo, Continuous Global Symmetries and Hyperweak Interactions in String Compactifications, JHEP 07 (2008) 073 [arXiv:0805.4037] [INSPIRE].
M. Goodsell, J. Jaeckel, J. Redondo and A. Ringwald, Naturally Light Hidden Photons in LARGE Volume String Compactifications, JHEP 11 (2009) 027 [arXiv:0909.0515] [INSPIRE].
M. Bullimore, J.P. Conlon and L.T. Witkowski, Kinetic mixing of U(1)s for local string models, JHEP 11 (2010) 142 [arXiv:1009.2380] [INSPIRE].
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, JHEP 07 (2011) 114 [arXiv:1103.3705] [INSPIRE].
R. Blumenhagen, Gauge Coupling Unification in F-theory Grand Unified Theories, Phys. Rev. Lett. 102 (2009) 071601 [arXiv:0812.0248] [INSPIRE].
J.J. Heckman, A. Tavanfar and C. Vafa, The Point of E 8 in F-theory GUTs, JHEP 08 (2010) 040 [arXiv:0906.0581] [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, Monodromies, Fluxes and Compact Three-Generation F-theory GUTs, JHEP 08 (2009) 046 [arXiv:0906.4672] [INSPIRE].
J.P. Conlon and E. Palti, On Gauge Threshold Corrections for Local IIB/F-theory GUTs, Phys. Rev. D 80 (2009) 106004 [arXiv:0907.1362] [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, Compact F-theory GUTs with U(1) (PQ), JHEP 04 (2010) 095 [arXiv:0912.0272] [INSPIRE].
E. Dudas and E. Palti, Froggatt-Nielsen models from E 8 in F-theory GUTs, JHEP 01 (2010) 127 [arXiv:0912.0853] [INSPIRE].
S. King, G. Leontaris and G. Ross, Family symmetries in F-theory GUTs, Nucl. Phys. B 838 (2010) 119 [arXiv:1005.1025] [INSPIRE].
E. Dudas and E. Palti, On hypercharge flux and exotics in F-theory GUTs, JHEP 09 (2010) 013 [arXiv:1007.1297] [INSPIRE].
J. Marsano, Hypercharge Flux, Exotics and Anomaly Cancellation in F-theory GUTs, Phys. Rev. Lett. 106 (2011) 081601 [arXiv:1011.2212] [INSPIRE].
C. Lüdeling, H.P. Nilles and C.C. Stephan, The Potential Fate of Local Model Building, Phys. Rev. D 83 (2011) 086008 [arXiv:1101.3346] [INSPIRE].
M.J. Dolan, J. Marsano, N. Saulina and S. Schäfer-Nameki, F-theory GUTs with U(1) Symmetries: Generalities and Survey, Phys. Rev. D 84 (2011) 066008 [arXiv:1102.0290] [INSPIRE].
L.E. Ibáñez, R. Rabadán and A. Uranga, Anomalous U(1)’s in type-I and type IIB D = 4, N =1 string vacua, Nucl. Phys. B 542(1999)112 [hep-th/9808139] [INSPIRE].
E. Poppitz, On the one loop Fayet-Iliopoulos term in chiral four-dimensional type-I orbifolds, Nucl. Phys. B 542 (1999) 31 [hep-th/9810010] [INSPIRE].
G. Aldazabal, S. Franco, L.E. Ibáñez, R. Rabadán and A. Uranga, D = 4 chiral string compactifications from intersecting branes, J. Math. Phys. 42 (2001) 3103 [hep-th/0011073] [INSPIRE].
H. Jockers and J. Louis, The Effective action of D7-branes in N = 1 Calabi-Yau orientifolds, Nucl. Phys. B 705 (2005) 167 [hep-th/0409098] [INSPIRE].
E. Plauschinn, The Generalized Green-Schwarz Mechanism for Type IIB Orientifolds with D3- and D7-branes, JHEP 05 (2009) 062 [arXiv:0811.2804] [INSPIRE].
T.W. Grimm, The N = 1 effective action of F-theory compactifications, Nucl. Phys. B 845 (2011) 48 [arXiv:1008.4133] [INSPIRE].
T.W. Grimm and J. Louis, The Effective action of N = 1 Calabi-Yau orientifolds, Nucl. Phys. B 699 (2004) 387 [hep-th/0403067] [INSPIRE].
T.W. Grimm, The Effective action of type-II Calabi-Yau orientifolds, Fortsch. Phys. 53 (2005) 1179 [hep-th/0507153] [INSPIRE].
D.S. Freed and E. Witten, Anomalies in string theory with D-branes, Asian J. Math 3 (1999)819 [hep-th/9907189] [INSPIRE].
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].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992), pg. 259.
J.P. Conlon, A. Maharana and F. Quevedo, Towards Realistic String Vacua, JHEP 05 (2009) 109 [arXiv:0810.5660] [INSPIRE].
A. Collinucci, F. Denef and M. Esole, D-brane Deconstructions in IIB Orientifolds, JHEP 02 (2009) 005 [arXiv:0805.1573] [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. Gurrieri, J. Louis, A. Micu and D. Waldram, Mirror symmetry in generalized Calabi-Yau compactifications, Nucl. Phys. B 654 (2003) 61 [hep-th/0211102] [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].
M. Graña, Flux compactifications in string theory: A Comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
K. Becker and M. Becker, M theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [INSPIRE].
T.W. Grimm and A. Klemm, U(1) Mediation of Flux Supersymmetry Breaking, JHEP 10 (2008) 077 [arXiv:0805.3361] [INSPIRE].
P.G. Camara, L.E. Ibáñez and F. Marchesano, RR photons, arXiv:1106.0060 [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, arXiv:1011.6388 [INSPIRE].
A. Collinucci, New F-theory lifts, JHEP 08 (2009) 076 [arXiv:0812.0175] [INSPIRE].
A. Collinucci, New F-theory lifts. II. Permutation orientifolds and enhanced singularities, JHEP 04 (2010) 076 [arXiv:0906.0003] [INSPIRE].
R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, F-theory uplifts and GUTs, JHEP 09 (2009) 053 [arXiv:0906.0013] [INSPIRE].
M. Berg, M. Haack and H. Samtleben, Calabi-Yau fourfolds with flux and supersymmetry breaking, JHEP 04 (2003) 046 [hep-th/0212255] [INSPIRE].
M. Haack and J. Louis, Duality in heterotic vacua with four supercharges, Nucl. Phys. B 575 (2000) 107 [hep-th/9912181] [INSPIRE].
T. House and A. Micu, M-Theory compactifications on manifolds with G 2 structure, Class. Quant. Grav. 22 (2005) 1709 [hep-th/0412006] [INSPIRE].
T. House and E. Palti, Effective action of (massive) IIA on manifolds with SU(3) structure, Phys. Rev. D 72 (2005) 026004 [hep-th/0505177] [INSPIRE].
M. Graña, J. Louis and D. Waldram, Hitchin functionals in N = 2 supergravity, JHEP 01 (2006) 008 [hep-th/0505264] [INSPIRE].
I. Benmachiche and T.W. Grimm, Generalized N = 1 orientifold compactifications and the Hitchin functionals, Nucl. Phys. B 748 (2006) 200 [hep-th/0602241] [INSPIRE].
T.W. Grimm and R. Savelli, Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds, arXiv:1109.3191 [INSPIRE].
K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].
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].
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].
S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4 − D N = 2 gauge theories: 1., Adv. Theor. Math. Phys. 1 (1998) 53 [hep-th/9706110] [INSPIRE].
S.H. Katz, D.R. Morrison and M. Plesser, Enhanced gauge symmetry in type-II string theory, Nucl. Phys. B 477 (1996) 105 [hep-th/9601108] [INSPIRE].
B.R. Greene, D.R. Morrison and A. Strominger, Black hole condensation and the unification of string vacua, Nucl. Phys. B 451 (1995) 109 [hep-th/9504145] [INSPIRE].
J.M. Maldacena, G.W. Moore and N. Seiberg, D-brane charges in five-brane backgrounds, JHEP 10 (2001) 005 [hep-th/0108152] [INSPIRE].
T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
M.B. Gonzalez, L.E. Ibáñez, P. Soler and A.M. Uranga, Discrete gauge symmetries in D-brane models, arXiv:1106.4169 [INSPIRE].
E. Witten, Nonperturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [INSPIRE].
R. Blumenhagen, A. Collinucci and B. Jurke, On Instanton Effects in F-theory, JHEP 08 (2010) 079 [arXiv:1002.1894] [INSPIRE].
M. Cvetič, I. Garcia-Etxebarria and J. Halverson, Global F-theory Models: Instantons and Gauge Dynamics, JHEP 01 (2011) 073 [arXiv:1003.5337] [INSPIRE].
R. Donagi and M. Wijnholt, MSW Instantons, arXiv:1005.5391 [INSPIRE].
M. Cvetič, I. Garcia-Etxebarria and J. Halverson, On the computation of non-perturbative effective potentials in the string theory landscape: IIB/F-theory perspective, arXiv:1009.5386 [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, On G-flux, M5 instantons and U(1)s in F-theory, arXiv:1107.1718 [INSPIRE].
M. Cvetič, J. Halverson and I. Garcia-Etxebarria, Three Looks at Instantons in F-theory - New Insights from Anomaly Inflow, String Junctions and Heterotic Duality, arXiv:1107.2388 [INSPIRE].
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Grimm, T.W., Kerstan, M., Palti, E. et al. Massive Abelian gauge symmetries and fluxes in F-theory. J. High Energ. Phys. 2011, 4 (2011). https://doi.org/10.1007/JHEP12(2011)004
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DOI: https://doi.org/10.1007/JHEP12(2011)004