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 K3 surface that is the double cover of ℂℙ2. 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 4D 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 K3 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 6D N = 1 supergravities, JHEP 12 (2009) 050 [arXiv:0910.1586] [INSPIRE].
V. Kumar, D.R. Morrison and W. Taylor, Mapping 6D 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 6D N = 1 supergravities, JHEP 11 (2010) 118 [arXiv:1008.1062] [INSPIRE].
V. Kumar, D.S. Park and W. Taylor, 6D supergravity without tensor multiplets, JHEP 04 (2011) 080 [arXiv:1011.0726] [INSPIRE].
N. Seiberg and W. Taylor, Charge lattices and consistency of 6D supergravity, JHEP 06 (2011) 001 [arXiv:1103.0019] [INSPIRE].
S. Monnier, G.W. Moore and D.S. Park, Quantization of anomaly coefficients in 6D \( \mathcal{N}=\left(1,0\right) \) supergravity, JHEP 02 (2018) 020 [arXiv:1711.04777] [INSPIRE].
W. Taylor and A.P. Turner, An infinite swampland of U(1) charge spectra in 6D 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 6D 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, E6 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 D3- and D7-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, D7-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, D7-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