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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. 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. 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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Modularity from monodromy
journal, May 2019


Generic matter representations in 6D supergravity theories
journal, May 2019

  • Taylor, Washington; Turner, Andrew P.
  • Journal of High Energy Physics, Vol. 2019, Issue 5
  • DOI: 10.1007/jhep05(2019)081

Phases of 5d SCFTs from M-/F-theory on non-flat fibrations
journal, May 2019

  • Apruzzi, Fabio; Lin, Ling; Mayrhofer, Christoph
  • Journal of High Energy Physics, Vol. 2019, Issue 5
  • DOI: 10.1007/jhep05(2019)187

The arithmetic of elliptic fibrations in gauge theories on a circle
journal, June 2016

  • Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/jhep06(2016)112

An infinite swampland of U(1) charge spectra in 6D supergravity theories
journal, June 2018

  • Taylor, Washington; Turner, Andrew P.
  • Journal of High Energy Physics, Vol. 2018, Issue 6
  • DOI: 10.1007/jhep06(2018)010

F-theory and all things rational: surveying U(1) symmetries with rational sections
journal, September 2015

  • Lawrie, Craig; Schäfer-Nameki, Sakura; Wong, Jin-Mann
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/jhep09(2015)144

Hidden selection rules, M5-instantons and fluxes in F-theory
journal, October 2015


Tall sections from non-minimal transformations
journal, October 2016

  • Morrison, David R.; Park, Daniel S.
  • Journal of High Energy Physics, Vol. 2016, Issue 10
  • DOI: 10.1007/jhep10(2016)033

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

Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities
journal, November 2019

  • Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten
  • Journal of High Energy Physics, Vol. 2019, Issue 11
  • DOI: 10.1007/jhep11(2019)170

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

Weak coupling limit of F-theory models with MSSM spectrum and massless U(1)’s
journal, March 2018

  • Mayorga Peña, Damián Kaloni; Valandro, Roberto
  • Journal of High Energy Physics, Vol. 2018, Issue 3
  • DOI: 10.1007/jhep03(2018)107

F-theory and 2d (0, 2) theories
journal, May 2016

  • Schäfer-Nameki, Sakura; Weigand, Timo
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/jhep05(2016)059

The toric SO(10) F-theory landscape
journal, December 2017

  • Buchmüller, W.; Dierigl, M.; Oehlmann, P. -K.
  • Journal of High Energy Physics, Vol. 2017, Issue 12
  • DOI: 10.1007/jhep12(2017)035

Complete Intersection Fibers in F-Theory
preprint, January 2014


F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections
text, January 2015


Tall sections from non-minimal transformations
text, January 2016


Gauge Backgrounds and Zero-Mode Counting in F-Theory
text, January 2017


The Toric SO(10) F-Theory Landscape
text, January 2017


6d SCFTs and U(1) Flavour Symmetries
text, January 2018


High U(1) charges in type IIB models and their F-theory lift
preprint, January 2018


Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
text, January 2018


Modularity from Monodromy
text, January 2019