Abstract
We consider phenomenological aspects of a natural class of Standard Model-like supersymmetric F-theory vacua realized through flux breaking of rigid E7 gauge factors. Three generations of Standard Model matter are realized in many of these vacua. We further find that many other Standard Model-like features are naturally compatible with these constructions. For example, dimension-4 and 5 terms associated with proton decay are ubiquitously suppressed. Many of these features are due to the group theoretical structure of E7 and associated F-theory geometry. In particular, a set of approximate global symmetries descends from the E7 group, leading to exponential suppression of undesired couplings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Taylor and Y.-N. Wang, The F-theory geometry with most flux vacua, JHEP 12 (2015) 164 [arXiv:1511.03209] [INSPIRE].
M. Cvetič, J. Halverson, G. Shiu and W. Taylor, Snowmass White Paper: String Theory and Particle Physics, arXiv:2204.01742 [INSPIRE].
F. Marchesano, B. Schellekens and T. Weigand, D-brane and F-theory Model Building, arXiv:2212.07443 [INSPIRE].
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. I, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. II, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
T. Weigand, F-theory, PoS TASI2017 (2018) 016 [arXiv:1806.01854] [INSPIRE].
J.J. Heckman, Particle Physics Implications of F-theory, Ann. Rev. Nucl. Part. Sci. 60 (2010) 237 [arXiv:1001.0577] [INSPIRE].
S.Y. Li and W. Taylor, Natural F-theory constructions of standard model structure from E7 flux breaking, Phys. Rev. D 106 (2022) L061902 [arXiv:2112.03947] [INSPIRE].
S.Y. Li and W. Taylor, Gauge symmetry breaking with fluxes and natural Standard Model structure from exceptional GUTs in F-theory, JHEP 11 (2022) 089 [arXiv:2207.14319] [INSPIRE].
M. Bies et al., Root bundles and towards exact matter spectra of F-theory MSSMs, JHEP 09 (2021) 076 [arXiv:2102.10115] [INSPIRE].
M. Bies, M. Cvetič and M. Liu, Statistics of limit root bundles relevant for exact matter spectra of F-theory MSSMs, Phys. Rev. D 104 (2021) L061903 [arXiv:2104.08297] [INSPIRE].
M. Bies, M. Cvetič, R. Donagi and M. Ong, Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models, JHEP 11 (2022) 004 [arXiv:2205.00008] [INSPIRE].
M. Bies, Root bundles: Applications to F-theory Standard Models, Proc. Symp. Pure Math. 107 (2024) 17 [arXiv:2303.08144] [INSPIRE].
M. Bies, M. Cvetič, R. Donagi and M. Ong, Improved statistics for F-theory standard models, arXiv:2307.02535 [INSPIRE].
M. Cvetič et al., Yukawa Hierarchies in Global F-theory Models, JHEP 01 (2020) 037 [arXiv:1906.10119] [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].
W. Taylor, Y.-N. Wang and Y. Yu, work in progress.
S. Andriolo, S.Y. Li and S.-H.H. Tye, String Landscape and Fermion Masses, Phys. Rev. D 101 (2020) 066005 [arXiv:1902.06608] [INSPIRE].
A.P. Braun and T. Watari, Distribution of the Number of Generations in Flux Compactifications, Phys. Rev. D 90 (2014) 121901 [arXiv:1408.6156] [INSPIRE].
W. Taylor and Y.-N. Wang, A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua, JHEP 01 (2016) 137 [arXiv:1510.04978] [INSPIRE].
R. Donagi and M. Wijnholt, Model Building with F-Theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [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, Adv. Theor. Math. Phys. 15 (2011) 1523 [arXiv:0808.2223] [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].
J. Marsano, N. Saulina and S. Schäfer-Nameki, Compact F-theory GUTs with U(1) (PQ), JHEP 04 (2010) 095 [arXiv:0912.0272] [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].
S. Krause, C. Mayrhofer and T. Weigand, G4 flux, chiral matter and singularity resolution in F-theory compactifications, Nucl. Phys. B 858 (2012) 1 [arXiv:1109.3454] [INSPIRE].
V. Braun, T.W. Grimm and J. Keitel, Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors, JHEP 12 (2013) 069 [arXiv:1306.0577] [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].
C.-M. Chen and Y.-C. Chung, On F-theory E6 GUTs, JHEP 03 (2011) 129 [arXiv:1010.5536] [INSPIRE].
J.C. Callaghan and S.F. King, E6 Models from F-theory, JHEP 04 (2013) 034 [arXiv:1210.6913] [INSPIRE].
J.C. Callaghan, S.F. King and G.K. Leontaris, Gauge coupling unification in E6 F-theory GUTs with matter and bulk exotics from flux breaking, JHEP 12 (2013) 037 [arXiv:1307.4593] [INSPIRE].
C. Mayrhofer, E. Palti and T. Weigand, Hypercharge Flux in IIB and F-theory: Anomalies and Gauge Coupling Unification, JHEP 09 (2013) 082 [arXiv:1303.3589] [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].
M. Buican et al., D-branes at Singularities, Compactification, and Hypercharge, JHEP 01 (2007) 107 [hep-th/0610007] [INSPIRE].
A.P. Braun and T. Watari, The Vertical, the Horizontal and the Rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications, JHEP 01 (2015) 047 [arXiv:1408.6167] [INSPIRE].
M. Cvetič et al., Quadrillion F-Theory Compactifications with the Exact Chiral Spectrum of the Standard Model, Phys. Rev. Lett. 123 (2019) 101601 [arXiv:1903.00009] [INSPIRE].
D. Klevers et al., F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches, JHEP 01 (2015) 142 [arXiv:1408.4808] [INSPIRE].
N. Raghuram, W. Taylor and A.P. Turner, General F-theory models with tuned (SU(3) × SU(2) × U(1))/ℤ6 symmetry, JHEP 04 (2020) 008 [arXiv:1912.10991] [INSPIRE].
P. Jefferson, W. Taylor and A.P. Turner, Chiral spectrum of the universal tuned (SU(3) × SU(2) × U(1))/ℤ6 4D F-theory model, JHEP 02 (2023) 254 [arXiv:2210.09473] [INSPIRE].
D.R. Morrison and W. Taylor, Classifying bases for 6D F-theory models, Central Eur. J. Phys. 10 (2012) 1072 [arXiv:1201.1943] [INSPIRE].
D.R. Morrison and W. Taylor, Non-Higgsable clusters for 4D F-theory models, JHEP 05 (2015) 080 [arXiv:1412.6112] [INSPIRE].
D.R. Morrison and W. Taylor, Toric bases for 6D F-theory models, Fortsch. Phys. 60 (2012) 1187 [arXiv:1204.0283] [INSPIRE].
P. Candelas et al., Codimension three bundle singularities in F theory, JHEP 06 (2002) 014 [hep-th/0009228] [INSPIRE].
C. Lawrie and S. Schäfer-Nameki, The Tate Form on Steroids: Resolution and Higher Codimension Fibers, JHEP 04 (2013) 061 [arXiv:1212.2949] [INSPIRE].
I. Achmed-Zade, I. García-Etxebarria and C. Mayrhofer, A note on non-flat points in the SU(5) × U(1)PQ F-theory model, JHEP 05 (2019) 013 [arXiv:1806.05612] [INSPIRE].
P. Jefferson, W. Taylor and A.P. Turner, Chiral Matter Multiplicities and Resolution-Independent Structure in 4D F-Theory Models, Commun. Math. Phys. 404 (2023) 1361 [arXiv:2108.07810] [INSPIRE].
P. Jefferson, S.Y. Li and W. Taylor, work in progress.
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, M. Kerstan, E. Palti and T. Weigand, Massive Abelian Gauge Symmetries and Fluxes in F-theory, JHEP 12 (2011) 004 [arXiv:1107.3842] [INSPIRE].
K. Kodaira, On compact analytic surfaces: II, Annals Math. 77 (1963) 563.
A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. IHES 21 (1964) 5.
T. Shioda, On elliptic modular surfaces, J. Math. Soc. Jap. 24 (1972) 20.
R. Wazir, Arithmetic on elliptic threefolds, Compos. Math. 140 (2004) 567 [math/0112259].
E. Witten, On flux quantization in M theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].
K. Becker and M. Becker, M theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [hep-th/9906070] [INSPIRE].
S. Sethi, C. Vafa and E. Witten, Constraints on low dimensional string compactifications, Nucl. Phys. B 480 (1996) 213 [hep-th/9606122] [INSPIRE].
T.W. Grimm and H. Hayashi, F-theory fluxes, Chirality and Chern-Simons theories, JHEP 03 (2012) 027 [arXiv:1111.1232] [INSPIRE].
T.W. Grimm and R. Savelli, Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds, Phys. Rev. D 85 (2012) 026003 [arXiv:1109.3191] [INSPIRE].
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].
S.Y. Li and W. Taylor, Large U(1) charges from flux breaking in 4D F-theory models, JHEP 02 (2023) 186 [arXiv:2211.11768] [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].
J. Marsano and S. Schäfer-Nameki, Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau’s, JHEP 11 (2011) 098 [arXiv:1108.1794] [INSPIRE].
M. Bies, C. Mayrhofer and T. Weigand, Gauge Backgrounds and Zero-Mode Counting in F-Theory, JHEP 11 (2017) 081 [arXiv:1706.04616] [INSPIRE].
M. Bies, C. Mayrhofer, C. Pehle and T. Weigand, Chow groups, Deligne cohomology and massless matter in F-theory, arXiv:1402.5144 [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].
M. Bershadsky et al., Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481 (1996) 215 [hep-th/9605200] [INSPIRE].
J.J. Heckman, D.R. Morrison and C. Vafa, On the Classification of 6D SCFTs and Generalized ADE Orbifolds, JHEP 05 (2014) 028 [Erratum ibid. 06 (2015) 017] [arXiv:1312.5746] [INSPIRE].
F. Apruzzi, J.J. Heckman, D.R. Morrison and L. Tizzano, 4D Gauge Theories with Conformal Matter, JHEP 09 (2018) 088 [arXiv:1803.00582] [INSPIRE].
E. Witten, Nonperturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [INSPIRE].
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.E. Ibanez and A.M. Uranga, Neutrino Majorana Masses from String Theory Instanton Effects, JHEP 03 (2007) 052 [hep-th/0609213] [INSPIRE].
R. Blumenhagen et al., Non-perturbative Yukawa Couplings from String Instantons, Phys. Rev. Lett. 100 (2008) 061602 [arXiv:0707.1871] [INSPIRE].
T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys. 383 (2021) 1669 [arXiv:1810.05338] [INSPIRE].
R. Tatar and T. Watari, Proton decay, Yukawa couplings and underlying gauge symmetry in string theory, Nucl. Phys. B 747 (2006) 212 [hep-th/0602238] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE].
L.E. Ibanez, F. Marchesano, D. Regalado and I. Valenzuela, The Intermediate Scale MSSM, the Higgs Mass and F-theory Unification, JHEP 07 (2012) 195 [arXiv:1206.2655] [INSPIRE].
A. Hebecker and J. Unwin, Precision Unification and Proton Decay in F-Theory GUTs with High Scale Supersymmetry, JHEP 09 (2014) 125 [arXiv:1405.2930] [INSPIRE].
E. Palti, Vector-Like Exotics in F-Theory and 750 GeV Diphotons, Nucl. Phys. B 907 (2016) 597 [arXiv:1601.00285] [INSPIRE].
J.J. Heckman and C. Vafa, Flavor Hierarchy From F-theory, Nucl. Phys. B 837 (2010) 137 [arXiv:0811.2417] [INSPIRE].
S. Cecotti, M.C.N. Cheng, J.J. Heckman and C. Vafa, Yukawa Couplings in F-theory and Non-Commutative Geometry, arXiv:0910.0477 [INSPIRE].
A. Font, L.E. Ibanez, F. Marchesano and D. Regalado, Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) Unification, JHEP 03 (2013) 140 [Erratum ibid. 07 (2013) 036] [arXiv:1211.6529] [INSPIRE].
A. Font, F. Marchesano, D. Regalado and G. Zoccarato, Up-type quark masses in SU(5) F-theory models, JHEP 11 (2013) 125 [arXiv:1307.8089] [INSPIRE].
F. Marchesano, D. Regalado and G. Zoccarato, Yukawa hierarchies at the point of E8 in F-theory, JHEP 04 (2015) 179 [arXiv:1503.02683] [INSPIRE].
F. Carta, F. Marchesano and G. Zoccarato, Fitting fermion masses and mixings in F-theory GUTs, JHEP 03 (2016) 126 [arXiv:1512.04846] [INSPIRE].
W. Taylor, D-brane field theory on compact spaces, Phys. Lett. B 394 (1997) 283 [hep-th/9611042] [INSPIRE].
S.P. Martin, A Supersymmetry primer, Adv. Ser. Direct. High Energy Phys. 18 (1998) 1 [hep-ph/9709356] [INSPIRE].
R. Blumenhagen, Gauge Coupling Unification in F-Theory Grand Unified Theories, Phys. Rev. Lett. 102 (2009) 071601 [arXiv:0812.0248] [INSPIRE].
M. Demirtas, C. Long, L. McAllister and M. Stillman, The Kreuzer-Skarke Axiverse, JHEP 04 (2020) 138 [arXiv:1808.01282] [INSPIRE].
V.I. Danilov and A.G. Khovanskiĭ, Newton polyhedra and an algorithm for computing hodge-deligne numbers, Math. USSR Izv. 29 (1987) 279.
P. Jefferson and M. Kim, On the intermediate Jacobian of M5-branes, arXiv:2211.00210 [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, P. Jefferson and M.J. Kang, Euler Characteristics of Crepant Resolutions of Weierstrass Models, Commun. Math. Phys. 371 (2019) 99 [arXiv:1703.00905] [INSPIRE].
L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: Rank one, JHEP 07 (2019) 178 [Addendum ibid. 01 (2020) 153] [arXiv:1809.01650] [INSPIRE].
A. Collinucci and R. Savelli, On Flux Quantization in F-Theory, JHEP 02 (2012) 015 [arXiv:1011.6388] [INSPIRE].
Acknowledgments
We would like to thank Lara Anderson, Martin Bies, Mirjam Cvetic, James Gray, Daniel Harlow, Jonathan Heckman, Patrick Jefferson, Manki Kim, Paul Oehlmann, Jesse Thaler, and Andrew Turner for helpful discussions. This work was supported by the DOE under contract #DE-SC00012567.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2401.00040
Rights and permissions
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.
About this article
Cite this article
Li, S.Y., Taylor, W. Towards natural and realistic E7 GUTs in F-theory. J. High Energ. Phys. 2024, 334 (2024). https://doi.org/10.1007/JHEP05(2024)334
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2024)334