Built on

S. Lang and A. Neron, Rational points of abelian varieties over function fields , American Journal of Mathematics 81
1959
Earlier work this paper cites.
Springer, 1986
J. H. Silverman, The Arithmetic of Elliptic Curves · 1986
Earlier work this paper cites.
J. Erler, Anomaly cancellation in six-dimensions , J. Math. Phys. 35
1994
Earlier work this paper cites.
D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 1 , Nucl. Phys. B473
1996
Earlier work this paper cites.
D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 2. , Nucl. Phys. B476
1996
Earlier work this paper cites.
M. Bershadsky, K. A. Intriligator, S. Kachru, D. R. Morrison, V. Sadov and C. Vafa, Geometric singularities and enhanced gauge symmetries , Nucl. Phys. B481
1996
Earlier work this paper cites.
V. Sadov, Generalized Green-Schwarz mechanism in F theory , Phys. Lett. B388
1996
Earlier work this paper cites.
S. H. Katz and C. Vafa, Matter from geometry , Nucl. Phys. B497
1997
Earlier work this paper cites.
R. Wazir, Arithmetic on elliptic threefolds , Compositio Mathematica 140
2004
Earlier work this paper cites.
American Mathematical Society, 2004
S. D. Cutkosky, Resolution of Singularities · 2004
Earlier work this paper cites.
F. Denef, Les Houches Lectures on Constructing String Vacua , in String theory and the real world: From particle physics to astrophysics. Proceedings, Summer School in Theoretical Physics, 87th Session, Les Houches, France, July 2-27, 2007 , pp. 483–610, 2008, 0803.1194 , https://inspirehep.net/record/780946/files/arXiv:0803.1194.pdf
Original
2008
Earlier work this paper cites.
T. W. Grimm and T. Weigand, On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs , Phys. Rev. D82
Original
2010
Earlier work this paper cites.
J. Marsano, N. Saulina and S. Schafer-Nameki, A Note on G-Fluxes for F-theory Model Building , JHEP 11
Original
2010
Earlier work this paper cites.
T. Weigand, Lectures on F-theory compactifications and model building , Class. Quant. Grav. 27
Original
2010
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M. J. Dolan, J. Marsano, N. Saulina and S. Schafer-Nameki, F-theory GUTs with U(1) Symmetries: Generalities and Survey , Phys. Rev. D84
Original
2011
Earlier work this paper cites.
M. J. Dolan, J. Marsano and S. Schafer-Nameki, Unification and Phenomenology of F-Theory GUTs with U ( 1 ) P Q U(1)_{P}Q , JHEP 12
Original
2011
Earlier work this paper cites.

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2017

Abelian F-theory Models with Charge-3 and Charge-4 Matter

Raghuram, Nikhil

Understand

This paper analyzes U(1) F-theory models admitting matter with charges $q=3$ and $4$.

First, we systematically derive a $q=3$ construction that generalizes the previous $q=3$ examples.
We argue that U(1) symmetries can be tuned through a procedure reminiscent of the SU(N) and Sp(N) tuning process.
For models with $q=3$ matter, the components of the generating section vanish to orders higher than 1 at the charge-3 matter loci.

Built on

S. Lang and A. Neron, Rational points of abelian varieties over function fields , American Journal of Mathematics 81
1959
Earlier work this paper cites.
Springer, 1986
J. H. Silverman, The Arithmetic of Elliptic Curves · 1986
Earlier work this paper cites.
J. Erler, Anomaly cancellation in six-dimensions , J. Math. Phys. 35
1994
Earlier work this paper cites.
D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 1 , Nucl. Phys. B473
1996
Earlier work this paper cites.
D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 2. , Nucl. Phys. B476
1996
Earlier work this paper cites.
M. Bershadsky, K. A. Intriligator, S. Kachru, D. R. Morrison, V. Sadov and C. Vafa, Geometric singularities and enhanced gauge symmetries , Nucl. Phys. B481
1996
Earlier work this paper cites.
V. Sadov, Generalized Green-Schwarz mechanism in F theory , Phys. Lett. B388
1996
Earlier work this paper cites.
S. H. Katz and C. Vafa, Matter from geometry , Nucl. Phys. B497
1997
Earlier work this paper cites.
R. Wazir, Arithmetic on elliptic threefolds , Compositio Mathematica 140
2004
Earlier work this paper cites.
American Mathematical Society, 2004
S. D. Cutkosky, Resolution of Singularities · 2004
Earlier work this paper cites.
F. Denef, Les Houches Lectures on Constructing String Vacua , in String theory and the real world: From particle physics to astrophysics. Proceedings, Summer School in Theoretical Physics, 87th Session, Les Houches, France, July 2-27, 2007 , pp. 483–610, 2008, 0803.1194 , https://inspirehep.net/record/780946/files/arXiv:0803.1194.pdf
Original
2008
Earlier work this paper cites.
T. W. Grimm and T. Weigand, On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs , Phys. Rev. D82
Original
2010
Earlier work this paper cites.
J. Marsano, N. Saulina and S. Schafer-Nameki, A Note on G-Fluxes for F-theory Model Building , JHEP 11
Original
2010
Earlier work this paper cites.
T. Weigand, Lectures on F-theory compactifications and model building , Class. Quant. Grav. 27
Original
2010
Earlier work this paper cites.
M. J. Dolan, J. Marsano, N. Saulina and S. Schafer-Nameki, F-theory GUTs with U(1) Symmetries: Generalities and Survey , Phys. Rev. D84
Original
2011
Earlier work this paper cites.
M. J. Dolan, J. Marsano and S. Schafer-Nameki, Unification and Phenomenology of F-Theory GUTs with U ( 1 ) P Q U(1)_{P}Q , JHEP 12
Original
2011
Earlier work this paper cites.