U(1) gauge symmetries in F-theory are expected to manifest themselves as codimension three singularities of Calabi-Yau fourfolds. However, some of these are known to become massive at strong coupling via the Stückelberg mechanism. In this note, we propose a geometric picture for detecting all U(1)’s, and determining which ones are massive and which ones are massless. We find that massive gauge symmetries show up as codimension three singularities that only admit small, non-Kähler, resolutions. Our proposal passes several highly non-trivial tests, including a case with a non-diagonal mass matrix.
M. Bershadsky et al., Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481 (1996) 215 [hep-th/9605200] [INSPIRE].
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].
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].
V. Braun, T.W. Grimm and J. Keitel, New global F-theory GUTs with U(1) symmetries, JHEP 09 (2013) 154 [arXiv:1302.1854] [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].
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, S. Franco, L.E. Ibáñez, R. Rabadán and A.M. Uranga, 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 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].
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].
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].
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].
T. Pantev and M. Wijnholt, Hitchin’s equations and M-theory phenomenology, J. Geom. Phys. 61 (2011) 1223 [arXiv:0905.1968] [INSPIRE].
T.W. Grimm and T.G. Pugh, Gauged supergravities and their symmetry-breaking vacua in F-theory, JHEP 06 (2013) 012 [arXiv:1302.3223] [INSPIRE].
A. Sen, Orientifold limit of F-theory vacua, Phys. Rev. D 55 (1997) 7345 [hep-th/9702165] [INSPIRE].
A. Sen, F-theory and the Gimon-Polchinski orientifold, Nucl. Phys. B 498 (1997) 135 [hep-th/9702061] [INSPIRE].
A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
A. Clingher, R. Donagi and M. Wijnholt, The Sen limit, arXiv:1212.4505 [INSPIRE].
R. Donagi, S. Katz and M. Wijnholt, Weak coupling, degeneration and log Calabi-Yau spaces, arXiv:1212.0553 [INSPIRE].
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].
P. Berglund, A. Klemm, P. Mayr and S. Theisen, On type IIB vacua with varying coupling constant, Nucl. Phys. B 558 (1999) 178 [hep-th/9805189] [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].
M. Buican, D. Malyshev, D.R. Morrison, H. Verlinde and M. Wijnholt, D-branes at singularities, compactification and hypercharge, JHEP 01 (2007) 107 [hep-th/0610007] [INSPIRE].
R. Donagi and M. Wijnholt, Higgs bundles and UV completion in F-theory, Commun. Math. Phys. 326 (2014) 287 [arXiv:0904.1218] [INSPIRE].
A. Collinucci, New F-theory lifts. II. Permutation orientifolds and enhanced singularities, JHEP 04 (2010) 076 [arXiv:0906.0003] [INSPIRE].
S. Krause, C. Mayrhofer and T. Weigand, Gauge fluxes in F-theory and type IIB orientifolds, JHEP 08 (2012) 119 [arXiv:1202.3138] [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].
P. Aluffi and M. Esole, New orientifold weak coupling limits in F-theory, JHEP 02 (2010) 020 [arXiv:0908.1572] [INSPIRE].
M. Esole and R. Savelli, Tate form and weak coupling limits in F-theory, JHEP 06 (2013) 027 [arXiv:1209.1633] [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].
R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, F-theory uplifts and GUTs, JHEP 09 (2009) 053 [arXiv:0906.0013] [INSPIRE].
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.
ArXiv ePrint: 1402.4054
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Braun, A.P., Collinucci, A. & Valandro, R. The fate of U(1)’s at strong coupling in F-theory. J. High Energ. Phys. 2014, 28 (2014). https://doi.org/10.1007/JHEP07(2014)028
- Differential and Algebraic Geometry