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Title: F-theory on all toric hypersurface fibrations and its Higgs branches

Abstract

We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in $$\mathbb P^{2}$$, $$\mathbb P^{1}$$ × $$\mathbb P^{1}$$ and the recently studied $$\mathbb P^{2}$$ (1,1, 2) , yield F-theory realizations of SUGRA theories with discrete gauge groups $$\mathbb Z$$3, $$\mathbb Z$$2 and $$\mathbb Z$$4.This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I 2-fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. Here, we also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP 1 has a U(1)-gauge field induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q = 3.

Authors:
 [1];  [2];  [2];  [3];  [2]
  1. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy; European Organization for Nuclear Research (CERN), Geneva (Switzerland). Dept. of Physics, Theory Group
  2. Univ. of Bonn (Germany). Bethe Center for Theoretical Physics, Inst. der Physikalisches
  3. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy
Publication Date:
Research Org.:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science foundation (NSF)
OSTI Identifier:
1454515
Grant/Contract Number:  
SC0007901; PHY05-51164
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; F-Theory; Differential and Algebraic Geometry; Discrete and Finite Symmetries; Supergravity Models

Citation Formats

Klevers, Denis, Mayorga Pena, Damian Kaloni, Oehlmann, Paul-Konstantin, Piragua, Hernan, and Reuter, Jonas. F-theory on all toric hypersurface fibrations and its Higgs branches. United States: N. p., 2015. Web. doi:10.1007/JHEP01(2015)142.
Klevers, Denis, Mayorga Pena, Damian Kaloni, Oehlmann, Paul-Konstantin, Piragua, Hernan, & Reuter, Jonas. F-theory on all toric hypersurface fibrations and its Higgs branches. United States. doi:https://doi.org/10.1007/JHEP01(2015)142
Klevers, Denis, Mayorga Pena, Damian Kaloni, Oehlmann, Paul-Konstantin, Piragua, Hernan, and Reuter, Jonas. Tue . "F-theory on all toric hypersurface fibrations and its Higgs branches". United States. doi:https://doi.org/10.1007/JHEP01(2015)142. https://www.osti.gov/servlets/purl/1454515.
@article{osti_1454515,
title = {F-theory on all toric hypersurface fibrations and its Higgs branches},
author = {Klevers, Denis and Mayorga Pena, Damian Kaloni and Oehlmann, Paul-Konstantin and Piragua, Hernan and Reuter, Jonas},
abstractNote = {We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in $\mathbb P^{2}$, $\mathbb P^{1}$ × $\mathbb P^{1}$ and the recently studied $\mathbb P^{2}$ (1,1, 2) , yield F-theory realizations of SUGRA theories with discrete gauge groups $\mathbb Z$3, $\mathbb Z$2 and $\mathbb Z$4.This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I 2-fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. Here, we also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP 1 has a U(1)-gauge field induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q = 3.},
doi = {10.1007/JHEP01(2015)142},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2015,
place = {United States},
year = {2015},
month = {1}
}

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    General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure
    journal, November 2015

    • Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan
    • Journal of High Energy Physics, Vol. 2015, Issue 11
    • DOI: 10.1007/jhep11(2015)204

    Gauge backgrounds and zero-mode counting in F-theory
    journal, November 2017

    • Bies, Martin; Mayrhofer, Christoph; Weigand, Timo
    • Journal of High Energy Physics, Vol. 2017, Issue 11
    • DOI: 10.1007/jhep11(2017)081

    6d SCFTs and U(1) flavour symmetries
    journal, November 2018

    • Lee, Seung-Joo; Regalado, Diego; Weigand, Timo
    • Journal of High Energy Physics, Vol. 2018, Issue 11
    • DOI: 10.1007/jhep11(2018)147

    Discrete Abelian gauge symmetries and axions
    journal, July 2015


    Quadrillion F -Theory Compactifications with the Exact Chiral Spectrum of the Standard Model
    journal, September 2019


    The toric SO(10) F-theory landscape
    text, January 2017

    • Buchmüller, W.; Dierigl, M.; Oehlmann, Paul
    • Deutsches Elektronen-Synchrotron, DESY, Hamburg
    • DOI: 10.3204/pubdb-2017-13977