An F-theory realization of the chiral MSSM with ℤ2-parity

Journal of High Energy Physics, Sep 2018

Abstract Using F-theory we construct 4D \( \mathcal{N}=1 \) SUGRA theories with the Standard Model gauge group, three chiral generations, and matter parity in order to forbid all dimension four baryon and lepton number violating operators. The underlying geometries are derived by constructing smooth genus-one fibered Calabi-Yau fourfolds using toric tops that have a Jacobian fibration with rank one Mordell-Weil group and SU(3) × SU(2) singularities. The necessary gauge backgrounds on the smooth fourfolds are shown to be fully compatible with the quantization condition, including positive integer D3-tadpoles. This construction realizes for the first time a consistent UV completion of an MSSM-like model with matter parity in F-theory. Moreover our construction is general enough to also exhibit other relevant ℤ2 charge extensions of the MSSM such as lepton and baryon parity. Such models however are rendered inconsistent by non-integer fluxes, which are necessary for producing the exact MSSM chiral spectrum. These inconsistencies turn out to be intimately related to field theory considerations regarding a UV-embedding of the ℤ2 into a U(1) and the resulting discrete anomalies.

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An F-theory realization of the chiral MSSM with ℤ2-parity

Journal of High Energy Physics September 2018, 2018:89 | Cite as An F-theory realization of the chiral MSSM with ℤ2-parity AuthorsAuthors and affiliations Mirjam CvetičLing LinMuyang LiuPaul-Konstantin Oehlmann Open Access Regular Article - Theoretical Physics First Online: 17 September 2018 Received: 20 July 2018 Accepted: 02 September 2018 6 Downloads Abstract Using F-theory we construct 4D \( \mathcal{N}=1 \) SUGRA theories with the Standard Model gauge group, three chiral generations, and matter parity in order to forbid all dimension four baryon and lepton number violating operators. The underlying geometries are derived by constructing smooth genus-one fibered Calabi-Yau fourfolds using toric tops that have a Jacobian fibration with rank one Mordell-Weil group and SU(3) × SU(2) singularities. The necessary gauge backgrounds on the smooth fourfolds are shown to be fully compatible with the quantization condition, including positive integer D3-tadpoles. This construction realizes for the first time a consistent UV completion of an MSSM-like model with matter parity in F-theory. Moreover our construction is general enough to also exhibit other relevant ℤ2 charge extensions of the MSSM such as lepton and baryon parity. Such models however are rendered inconsistent by non-integer fluxes, which are necessary for producing the exact MSSM chiral spectrum. These inconsistencies turn out to be intimately related to field theory considerations regarding a UV-embedding of the ℤ2 into a U(1) and the resulting discrete anomalies. Keywords Discrete Symmetries F-Theory Flux compactifications Supersymmetric Standard Model  ArXiv ePrint: 1807.01320 Download to read the full article text Notes 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. References [1] C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [2] 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].ADSMathSciNetCrossRefGoogle Scholar [3] W. Taylor and Y.-N. Wang, The F-theory geometry with most flux vacua, JHEP 12 (2015) 164 [arXiv:1511.03209] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar [4] J. Halverson and J. Tian, Cost of seven-brane gauge symmetry in a quadrillion F-theory compactifications, Phys. Rev. D 95 (2017) 026005 [arXiv:1610.08864] [INSPIRE].ADSMathSciNetGoogle Scholar [5] J. Halverson, C. Long and B. Sung, Algorithmic universality in F-theory compactifications, Phys. Rev. D 96 (2017) 126006 [arXiv:1706.02299] [INSPIRE].ADSGoogle Scholar [6] W. Taylor, TASI Lectures on Supergravity and String Vacua in Various Dimensions, arXiv:1104.2051 [INSPIRE]. [7] T. Weigand, Lectures on F-theory compactifications and model building, Class. Quant. Grav. 27 (2010) 214004 [arXiv:1009.3497] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [8] A. Maharana and E. Palti, Models of Particle Physics from Type IIB String Theory and F-theory: A Review, Int. J. Mod. Phys. A 28 (2013) 1330005 [arXiv:1212.0555] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [9] T. Weigand, TASI Lectures on F-theory, arXiv:1806.01854 [INSPIRE]. [10] R. Donagi and M. Wijnholt, Model Building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].MathSciNetCrossRefGoogle Scholar [11] C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [12] 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].ADSMathSciNetCrossRefGoogle Scholar [13] R. Donagi and M. Wijnholt, Breaking GUT Groups in F-theory, Adv. Theor. Math. Phys. 15 (2011) 1523 [arXiv:0808.2223] [INSPIRE].MathSciNetCrossRefGoogle Scholar [14] E. Dudas and E. Palti, Froggatt-Nielsen models from E 8 in F-theory GUTs, JHEP 01 (2010) 127 [arXiv:0912.0853] [INSPIRE].ADSCrossRefGoogle Scholar [15] 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].ADSMathSciNetCrossRefGoogle Scholar [16] 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].ADSGoogle Scholar [17] 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].ADSMathSciNetCrossRefGoogle Scholar [18] M. Cvetič, T.W. Grimm and D. Klevers, Anomaly Cancellation And Abelian Gauge Symmetries In F-theory, JHEP 02 (2013) 101 [arXiv:12 (...truncated)


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Mirjam Cvetič, Ling Lin, Muyang Liu, Paul-Konstantin Oehlmann. An F-theory realization of the chiral MSSM with ℤ2-parity, Journal of High Energy Physics, 2018, pp. 89, Volume 2018, Issue 9, DOI: 10.1007/JHEP09(2018)089