skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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 twomore » 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.« less

Authors:
 [1];  [2];  [2];  [3];  [2]
+ Show Author Affiliations
  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:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
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.
Copy to clipboard
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
Copy to clipboard
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.
Copy to clipboard
@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},
url = {https://www.osti.gov/biblio/1454515}, journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 1,
volume = 2015,
place = {United States},
year = {2015},
month = {1}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1007/JHEP01(2015)142
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 70 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

New branches of string compactifications and their F-theory duals
journal, May 1997

Refined stable pair invariants for E-, M- and [p, q]-strings
journal, November 2013

Merging heterotic orbifolds and K3 compactifications with line bundles
journal, January 2007

U(1) symmetries in F-theory GUTs with multiple sections
journal, March 2013

Constraints on 6D supergravity theories with abelian gauge symmetry
journal, January 2012

The Tate form on steroids: resolution and higher codimension fibers
journal, April 2013

Enhanced gauge symmetry in type 11 string theory
journal, October 1996

Box graphs and singular fibers
journal, May 2014

Non-simply-connected gauge groups and rational points on elliptic curves
journal, July 1998

F-theory compactifications with multiple U(1)-factors: addendum
journal, December 2013

Vector Bundles and F Theory
journal, August 1997

Duality between the webs of heterotic and type II vacua
journal, February 1998

Jacobians of Genus One Curves
journal, October 2001

Froggatt-Nielsen models from E 8 in F-theory GUTs
journal, January 2010

Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections
journal, May 2005

Conifold transitions in $M$-theory on Calabi-Yau fourfolds with background fluxes
journal, January 2013

Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1)×U(1)×U(1) gauge symmetry
journal, March 2014

Rational Points of Abelian Varieties Over Function Fields
journal, January 1959

Effective action of 6D F-theory with U(1) factors: rational sections make Chern-Simons terms jump
journal, July 2013

Compactifications of F-theory on Calabi-Yau threefolds (II)
journal, September 1996

F-theory on Spin(7) manifolds: weak-coupling limit
journal, February 2014

Rational isogenies of prime degree
journal, June 1978

F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds
journal, October 2012

Global F-theory GUTs
journal, April 2010

The Cremmer-Scherk mechanism in F-theory compactifications on K3 manifolds
journal, May 2014

F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections
journal, June 2013

Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories
journal, May 2007

Modular curves and the eisenstein ideal
journal, December 1977

Model building with $F$-theory
journal, January 2011

The fate of U(1)’s at strong coupling in F-theory
journal, July 2014

Phase transitions in M-theory and F-theory
journal, July 1996

Anomalies and the Euler characteristic of elliptic Calabi–Yau threefolds
journal, January 2012

Evidence for F-theory
journal, June 1996

BPS states of exceptional non-critical strings
journal, September 1997

The <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> effective action of F-theory compactifications
journal, April 2011

Heterotic string/F-theory duality from mirror symmetry
journal, January 1998

Matter from geometry without resolution
journal, October 2013

Compactifications of F-theory on Calabi-Yau threefolds. (I)
journal, August 1996

New aspects of Heterotic–F-theory duality
journal, January 2009

GUTs and exceptional branes in F-theory — II. Experimental predictions
journal, January 2009

On finiteness of type IIB compactifications: magnetized branes on elliptic Calabi-Yau threefolds
journal, June 2014

Phases, flops and F-theory: SU(5) gauge theories
journal, October 2013

Small resolutions of SU(5)-models in F-theory
journal, January 2013

GUTs and exceptional branes in F-theory — I
journal, January 2009

Weierstrass models of elliptic toric $K3$ hypersurfaces and symplectic cuts
journal, January 2013

The landscape of intersecting brane models
journal, January 2007

F-theory fluxes, chirality and Chern-Simons theories
journal, March 2012

Geometric constraints in dual F-theory and heterotic string compactifications
journal, August 2014

Geometric engineering in toric F-theory and GUTs with U(1) gauge factors
journal, December 2013

6D supergravity without tensor multiplets
journal, April 2011

Chiral four-dimensional F-theory compactifications with SU(5) and multiple U(1)-factors
journal, April 2014

Proton decay in supersymmetric models
journal, May 1982

Anomaly cancellation and abelian gauge symmetries in F-theory
journal, February 2013

Yukawas, G-flux, and spectral covers from resolved Calabi-Yau’s
journal, November 2011

Tate’s algorithm and F-theory
journal, August 2011

Mapping 6D $ \mathcal{N} = 1 $ supergravities to F-theory
journal, February 2010

Rational F-theory GUTs without exotics
journal, July 2014

<mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mrow><mml:mi mathvariant="italic">SU</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>5</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> tops with multiple <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>s in F-theory
journal, May 2014

Global aspects of the space of 6D $ \mathcal{N} = 1 $ supergravities
journal, November 2010

Anomaly equations and intersection theory
journal, January 2012

Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties
journal, November 2012

-flux, chiral matter and singularity resolution in F-theory compactifications
journal, May 2012

F-theory on genus-one fibrations
journal, August 2014

On Compact Analytic Surfaces: II
journal, May 1963

Structure in 6D and 4D $ \mathcal{N}=1 $ supergravity theories from F-theory
journal, October 2012

Mordell-Weil torsion and the global structure of gauge groups in F-theory
journal, October 2014

Geometric singularities and enhanced gauge symmetries
journal, December 1996

Non-supersymmetric F-theory compactifications on Spin(7) manifolds
journal, January 2014

Affine Kac-Moody algebras, CHL strings and the classification of tops
journal, January 2003

Effective lagrangian description on discrete gauge symmetries
journal, August 1989

Classifying bases for 6D F-theory models
journal, January 2012

Discrete gauge symmetry in continuum theories
journal, March 1989

Massive Abelian gauge symmetries and fluxes in F-theory
journal, December 2011

On the classification of 6D SCFTs and generalized ADE orbifolds
journal, May 2014

Monodromies, fluxes, and compact three-generation F-theory GUTs
journal, August 2009

Toric bases for 6D F-theory models
journal, May 2012

Physics of F-theory compactifications without section
journal, December 2014

    [ × clear filter / sort ]

    Works referencing / citing this record:

    Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
    journal, February 2019

    Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
    journal, February 2019

    Modularity from monodromy
    journal, May 2019

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

    The global gauge group structure of F-theory compactification with U(1)s
    journal, January 2018

    Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
    journal, February 2019

    Complete intersection fibers in F-theory
    journal, March 2015

    Structure of stable degeneration of K3 surfaces into pairs of rational elliptic surfaces
    journal, March 2018

    Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications
    journal, March 2019

    High U(1) charges in type IIB models and their F-theory lift
    journal, April 2019

    A geometrical upper bound on the inflaton range
    journal, May 2018

    A note on non-flat points in the SU(5) × U(1)PQ F-theory model
    journal, May 2019

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

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

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

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

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

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

    Tall sections from non-minimal transformations
    journal, October 2016

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

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

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

    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

      [ × clear filter / sort ]

      Similar records in OSTI.GOV collections: