## Abstract

We construct models with U(1) gauge group and matter with charges up to 6, in the context of type IIB compactifications. We show explicitly that models with charges up to 4 can be derived from corresponding models in F-theory by applying the Sen weak coupling limit. We derive which type IIB models should be the limit of charge 5 and 6 F-theory models. Explicit six dimensional type IIB models with maximal charge 5 and 6 are constructed on an algebraic *K*3 surface that is the double cover of *ℂ*ℙ^{2}. By using type IIB results we are also able to rediscover the F-theory charge 4 model in a straightforward way.

## References

C. Vafa,

*Evidence for F-theory*,*Nucl. Phys.***B 469**(1996) 403 [hep-th/9602022] [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].C. Beasley, J.J. Heckman and C. Vafa,

*GUTs and exceptional branes in F-theory*—*I*,*JHEP***01**(2009) 058 [arXiv:0802.3391] [INSPIRE].R. Donagi and M. Wijnholt,

*Model building with F-theory*,*Adv. Theor. Math. Phys.***15**(2011) 1237 [arXiv:0802.2969] [INSPIRE].J. Halverson, C. Long and B. Sung,

*Algorithmic universality in F-theory compactifications*,*Phys. Rev.***D 96**(2017) 126006 [arXiv:1706.02299] [INSPIRE].W. Taylor and Y.-N. Wang,

*Scanning the skeleton of the*4*D F-theory landscape*,*JHEP***01**(2018) 111 [arXiv:1710.11235] [INSPIRE].V. Braun, T.W. Grimm and J. Keitel,

*Complete intersection fibers in F-theory*,*JHEP***03**(2015) 125 [arXiv:1411.2615] [INSPIRE].Y. Kimura,

*F-theory models on K*3*surfaces with various Mordell-Weil ranks*—*Constructions that use quadratic base change of rational elliptic surfaces*,*JHEP***05**(2018) 048 [arXiv:1802.05195] [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].M. Cvetič, T.W. Grimm and D. Klevers,

*Anomaly cancellation and abelian gauge symmetries in F-theory*,*JHEP***02**(2013) 101 [arXiv:1210.6034] [INSPIRE].C. Mayrhofer, E. Palti and T. Weigand, U(1)

*symmetries in F-theory GUTs with multiple sections*,*JHEP***03**(2013) 098 [arXiv:1211.6742] [INSPIRE].M. Cvetič, D. Klevers and H. Piragua,

*F-theory compactifications with multiple*U(1)*-factors: constructing elliptic fibrations with rational sections*,*JHEP***06**(2013) 067 [arXiv:1303.6970] [INSPIRE].M. Cvetič, D. Klevers, H. Piragua and P. Song,

*Elliptic fibrations with rank three Mordell-Weil group: F-theory with*U(1) × U(1) × U(1)*gauge symmetry*,*JHEP***03**(2014) 021 [arXiv:1310.0463] [INSPIRE].L.B. Anderson, I. García-Etxebarria, T.W. Grimm and J. Keitel,

*Physics of F-theory compactifications without section*,*JHEP***12**(2014) 156 [arXiv:1406.5180] [INSPIRE].D. Klevers et al.,

*F-theory on all toric hypersurface fibrations and its Higgs branches*,*JHEP***01**(2015) 142 [arXiv:1408.4808] [INSPIRE].C. Mayrhofer, E. Palti, O. Till and T. Weigand,

*Discrete gauge symmetries by higgsing in four-dimensional F-theory compactifications*,*JHEP***12**(2014) 068 [arXiv:1408.6831] [INSPIRE].L. Lin, C. Mayrhofer, O. Till and T. Weigand,

*Fluxes in F-theory compactifications on genus-one fibrations*,*JHEP***01**(2016) 098 [arXiv:1508.00162] [INSPIRE].M. Cvetič, A. Grassi and M. Poretschkin,

*Discrete symmetries in heterotic/F-theory duality and mirror symmetry*,*JHEP***06**(2017) 156 [arXiv:1607.03176] [INSPIRE].V. Kumar and W. Taylor,

*String universality in six dimensions*,*Adv. Theor. Math. Phys.***15**(2011) 325 [arXiv:0906.0987] [INSPIRE].V. Kumar and W. Taylor,

*A bound on*6*D N*= 1*supergravities*,*JHEP***12**(2009) 050 [arXiv:0910.1586] [INSPIRE].V. Kumar, D.R. Morrison and W. Taylor,

*Mapping*6*D N*= 1*supergravities to F-theory*,*JHEP***02**(2010) 099 [arXiv:0911.3393] [INSPIRE].V. Kumar, D.R. Morrison and W. Taylor,

*Global aspects of the space of*6*D N*= 1*supergravities*,*JHEP***11**(2010) 118 [arXiv:1008.1062] [INSPIRE].V. Kumar, D.S. Park and W. Taylor, 6

*D supergravity without tensor multiplets*,*JHEP***04**(2011) 080 [arXiv:1011.0726] [INSPIRE].N. Seiberg and W. Taylor,

*Charge lattices and consistency of*6*D supergravity*,*JHEP***06**(2011) 001 [arXiv:1103.0019] [INSPIRE].S. Monnier, G.W. Moore and D.S. Park,

*Quantization of anomaly coefficients in*6*D*\( \mathcal{N}=\left(1,0\right) \)*supergravity*,*JHEP***02**(2018) 020 [arXiv:1711.04777] [INSPIRE].W. Taylor and A.P. Turner,

*An infinite swampland of*U(1)*charge spectra in*6*D supergravity theories*,*JHEP***06**(2018) 010 [arXiv:1803.04447] [INSPIRE].A. Grassi and D.R. Morrison,

*Anomalies and the Euler characteristic of elliptic Calabi-Yau threefolds*,*Commun. Num. Theor. Phys.***6**(2012) 51 [arXiv:1109.0042] [INSPIRE].L.B. Anderson, J. Gray, N. Raghuram and W. Taylor,

*Matter in transition*,*JHEP***04**(2016) 080 [arXiv:1512.05791] [INSPIRE].D. Klevers, D.R. Morrison, N. Raghuram and W. Taylor,

*Exotic matter on singular divisors in F-theory*,*JHEP***11**(2017) 124 [arXiv:1706.08194] [INSPIRE].M. Cvetič, J.J. Heckman and L. Lin,

*Towards exotic matter and discrete non-Abelian symmetries in F-theory*,*JHEP***11**(2018) 001 [arXiv:1806.10594] [INSPIRE].D.S. Park and W. Taylor,

*Constraints on*6*D supergravity theories with abelian gauge symmetry*,*JHEP***01**(2012) 141 [arXiv:1110.5916] [INSPIRE].N. Raghuram and W. Taylor,

*Large*U(1)*charges in F-theory*,*JHEP***10**(2018) 182 [arXiv:1809.01666] [INSPIRE].N. Raghuram,

*Abelian F-theory models with charge-3 and charge-4 matter*,*JHEP***05**(2018) 050 [arXiv:1711.03210] [INSPIRE].A. Sen,

*Orientifold limit of F-theory vacua*,*Phys. Rev.***D 55**(1997) R7345 [hep-th/9702165] [INSPIRE].D.K. Mayorga Pena and R. Valandro,

*Weak coupling limit of F-theory models with MSSM spectrum and massless U(1)*’*s*,*JHEP***03**(2018) 107 [arXiv:1708.09452] [INSPIRE].R.L.E. Schwarzenberger,

*Vector bundles on algebraic surfaces*,*Proc. London Math. Soc.***11**(1961) 601.R. Friedman,

*Algebraic surfaces and holomorphic vector bundles*, Universitext, Springer, Germany (1998).S. Krause, C. Mayrhofer and T. Weigand,

*Gauge fluxes in F-theory and type IIB orientifolds*,*JHEP***08**(2012) 119 [arXiv:1202.3138] [INSPIRE].A. Collinucci and R. Savelli,

*On flux quantization in F-theory II: unitary and symplectic gauge groups*,*JHEP***08**(2012) 094 [arXiv:1203.4542] [INSPIRE].A.P. Braun, A. Collinucci and R. Valandro,

*The fate of*U(1)’*s at strong coupling in F-theory*,*JHEP***07**(2014) 028 [arXiv:1402.4054] [INSPIRE].A. Collinucci and I. García-Etxebarria,

*E*6*Yukawa couplings in F-theory as D-brane instanton effects*,*JHEP***03**(2017) 155 [arXiv:1612.06874] [INSPIRE].H. Jockers and W. Lerche,

*Matrix factorizations, D-branes and their deformations*,*Nucl. Phys. Proc. Suppl.***171**(2007) 196 [arXiv:0708.0157] [INSPIRE].A.P. Braun, A. Collinucci and R. Valandro,

*G-flux in F-theory and algebraic cycles*,*Nucl. Phys.***B 856**(2012) 129 [arXiv:1107.5337] [INSPIRE].A. Collinucci and R. Savelli,

*F-theory on singular spaces*,*JHEP***09**(2015) 100 [arXiv:1410.4867] [INSPIRE].A. Collinucci, M. Fazzi and R. Valandro,

*Geometric engineering on flops of length two*,*JHEP***04**(2018) 090 [arXiv:1802.00813].D.R. Morrison and D.S. Park,

*F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds*,*JHEP***10**(2012) 128 [arXiv:1208.2695] [INSPIRE].V.V. Batyrev,

*Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties*,*J. Alg. Geom.***3**(1994) 493 [alg-geom/9310003] [INSPIRE].M. Esole and R. Savelli,

*Tate form and weak coupling limits in F-theory*,*JHEP***06**(2013) 027 [arXiv:1209.1633] [INSPIRE].L.E. Ibáñez, R. Rabadán and A.M. 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 et al.,

*D*= 4*chiral string compactifications from intersecting branes*,*J. Math. Phys.***42**(2001) 3103 [hep-th/0011073] [INSPIRE].E. Plauschinn,

*The generalized Green-Schwarz mechanism for type IIB orientifolds with D*3*- and D*7*-branes*,*JHEP***05**(2009) 062 [arXiv:0811.2804] [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].T.W. Grimm, M. Kerstan, E. Palti and T. Weigand,

*Massive abelian gauge symmetries and fluxes in F-theory*,*JHEP***12**(2011) 004 [arXiv:1107.3842] [INSPIRE].A.P. Braun, A. Collinucci and R. Valandro,

*Hypercharge flux in F-theory and the stable Sen limit*,*JHEP***07**(2014) 121 [arXiv:1402.4096] [INSPIRE].J. Polchinski,

*Monopoles, duality and string theory*,*Int. J. Mod. Phys.***A 19S1**(2004) 145 [hep-th/0304042] [INSPIRE].T. Banks and N. Seiberg,

*Symmetries and strings in field theory and gravity*,*Phys. Rev.***D 83**(2011) 084019 [arXiv:1011.5120] [INSPIRE].A.P. Braun, S. Gerigk, A. Hebecker and H. Triendl,

*D*7*-brane moduli vs. F-theory cycles in elliptically fibred threefolds*,*Nucl. Phys.***B 836**(2010) 1 [arXiv:0912.1596] [INSPIRE].V.V. Nikulin,

*Discrete reflection groups in Lobachevsky spaces and algebraic surfaces*, in the proceedings of the*International Congress of Mathematicians (ICM 1986)*, August 3-11, Berkeley, U.S.A. (1986).A. Collinucci, F. Denef and M. Esole,

*D-brane deconstructions in IIB orientifolds*,*JHEP***02**(2009) 005 [arXiv:0805.1573] [INSPIRE].A.P. Braun, A. Hebecker and H. Triendl,

*D*7*-brane motion from M-theory cycles and obstructions in the weak coupling limit*,*Nucl. Phys.***B 800**(2008) 298 [arXiv:0801.2163] [INSPIRE].M. Cvetič, D. Klevers, H. Piragua and W. Taylor,

*General*U(1) × U(1)*F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure*,*JHEP***11**(2015) 204 [arXiv:1507.05954] [INSPIRE].Y. Kimura,

*Discrete gauge groups in F-theory models on genus-one fibered Calabi-Yau*4*-folds without section*,*JHEP***04**(2017) 168 [arXiv:1608.07219] [INSPIRE].D.S. Park,

*Anomaly equations and intersection theory*,*JHEP***01**(2012) 093 [arXiv:1111.2351] [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: 1811.11777

## Rights and permissions

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

## About this article

### Cite this article

Cianci, F.M., Mayorga Peña, D.K. & Valandro, R. High U(1) charges in type IIB models and their F-theory lift.
*J. High Energ. Phys.* **2019**, 12 (2019). https://doi.org/10.1007/JHEP04(2019)012

Received:

Accepted:

Published:

DOI: https://doi.org/10.1007/JHEP04(2019)012

### Keywords

- Anomalies in Field and String Theories
- D-branes
- Field Theories in Higher Dimensions
- Superstring Vacua