Toric Construction of Global F-Theory GUTs

Christoph Mayrhofer; Johanna Knapp; Maximilian Kreuzer; Nils-Ole Walliser

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Toric Construction of Global F-Theory GUTs

Johanna Knapp, Maximilian Kreuzer, Christoph Mayrhofer, Nils-Ole Walliser

High Energy Physics - Theory · Submitted 25 Jan 2011

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The authors' main claim We find that elementary conditions which are motivated by F-theory GUTs lead to strong constraints on the geometry, which significantly reduce the number of suitable models.

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arXiv ID1101.4908 (version 2)

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CitationChristoph Mayrhofer, Johanna Knapp, Maximilian Kreuzer, Nils-Ole Walliser. "Toric Construction of Global F-Theory GUTs." arXiv:1101.4908 (2011). https://pith.science/paper/P6YITTXW

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We systematically construct a large number of compact Calabi-Yau fourfolds which are suitable for F-theory model building. These elliptically fibered Calabi-Yaus are complete intersections of two hypersurfaces in a six dimensional ambient space. We first construct three-dimensional base manifolds that are hypersurfaces in a toric ambient space. We search for divisors which can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations over these base manifolds. We find that elementary conditions which are motivated by F-theory GUTs lead to strong constraints on the geometry, which significantly reduce the number of suitable models. The complete database of models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out several examples in more detail.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We systematically construct a large number of compact Calabi-Yau fourfolds which are suitable for F-theory model building.	contribution 1.00	0.96	0.14	asserted 1.00
s1	These elliptically fibered Calabi-Yaus are complete intersections of two hypersurfaces in a six dimensional ambient space.	method 0.54	0.65	0.04	asserted 1.00
s2	We first construct three-dimensional base manifolds that are hypersurfaces in a toric ambient space.	method 0.98	0.94	0.03	asserted 1.00
s3	We search for divisors which can support an F-theory GUT.	method 0.85	0.92	0.04	asserted 0.88
s4	The fourfolds are obtained as elliptic fibrations over these base manifolds.	method 0.96	0.86	0.06	asserted 1.00
s5	We find that elementary conditions which are motivated by F-theory GUTs lead to strong constraints on the geometry, which significantly reduce the number of suitable models.	result 0.98	0.96	0.69	asserted 1.00
s6	The complete database of models is available at http://hep.itp.tuwien.ac.at/f-theory/.	contribution 0.86	0.51	0.03	asserted 0.99
s7	We work out several examples in more detail.	contribution 0.80	0.95	0.04	asserted 0.99

What kind of paper the classifier reports this is: dataset or benchmark 0.83 · evidence from proof or derivation 0.62.

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Original abstract

We systematically construct a large number of compact Calabi-Yau fourfolds which are suitable for F-theory model building. These elliptically fibered Calabi-Yaus are complete intersections of two hypersurfaces in a six dimensional ambient space. We first construct three-dimensional base manifolds that are hypersurfaces in a toric ambient space. We search for divisors which can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations over these base manifolds. We find that elementary conditions which are motivated by F-theory GUTs lead to strong constraints on the geometry, which significantly reduce the number of suitable models. The complete database of models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out several examples in more detail.

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Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors
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A systematic toric algorithm classifies all SU(5) F-theory GUTs with U(1) factors and proves that hypersurface models force all 10-matter fields to share one U(1) charge.
New Global F-theory GUTs with U(1) symmetries
hep-th 2013-02 conditional novelty 7.0 of 10

An explicit F-theory compactification on a resolved Calabi-Yau fourfold yields an SU(5)×U(1) GUT whose matter spectrum does not descend from E8 and evades the hypercharge-flux no-go theorem.
Toric bases for 6D F-theory models
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A complete computer enumeration finds 61,539 toric bases for 6D F-theory, with tensor multiplet number from 0 to 193, and confirms that the toric monomial count reproduces the gravitational anomaly condition on every base.
Gauge Fluxes in F-theory and Type IIB Orientifolds
hep-th 2012-02 accept novelty 7.0 of 10

The universal spectral cover flux of F-theory SU(5) models is identified with the Type IIB gauge flux of the massive diagonal U(1), and the extra massless U(1) flux is matched to a specific linear combination of brane fluxes.
Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
hep-th 2011-08 accept novelty 7.0 of 10

An explicit resolution of elliptically fibered Calabi-Yau fourfolds with A4 singularities yields exact Chern classes, proves a conjectured Euler-characteristic shift, and derives the local Higgs-bundle spectral cover ...

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Chow groups, Deligne cohomology and massless matter in F-theory
hep-th 2014-02 conditional novelty 6.0 of 10

A Chow-group and Deligne-cohomology construction extracts a line bundle on each F-theory matter curve whose cohomology groups are conjectured to count the exact charged massless spectrum.
SU(5) Tops with Multiple U(1)s in F-theory
hep-th 2013-07 accept novelty 6.0 of 10

Four inequivalent SU(5) x U(1) x U(1) F-theory models are built on Bl2P2[3] fibrations, and one is shown to require Yukawa couplings that no Higgsing of E8 can produce.
Matter From Geometry Without Resolution
hep-th 2013-06 conditional novelty 6.0 of 10

Deforming ADE singularities of an elliptic fibration, instead of resolving them, reproduces the root lattices and high-dimensional representations of the corresponding Lie algebras and the monodromy reduction D4 to G2.
Anomaly Cancellation And Abelian Gauge Symmetries In F-theory
hep-th 2012-10 conditional novelty 6.0 of 10

F-theory fluxes automatically implement the four-dimensional Green-Schwarz mechanism, and the mixed Abelian-gravitational anomaly is the coefficient of a three-dimensional Chern-Simons term for the Kaluza-Klein vector.
Brane Tilings and Reflexive Polygons
hep-th 2012-01 conditional novelty 6.0 of 10

Exactly 30 brane tilings realize the 16 reflexive polygons as mesonic moduli spaces, and for each one the lattice of mesonic generator charges is the polar dual reflexive polygon of the toric diagram.
G_4 flux, chiral matter and singularity resolution in F-theory compactifications
hep-th 2011-09 conditional novelty 6.0 of 10

A U(1)-restricted F-theory compactification with SU(5) gauge group yields chirality-inducing G4 fluxes whose chiral index equals the U(1) charge times the flux integral over the matter curve, realized in an explicit t...
G-flux in F-theory and algebraic cycles
hep-th 2011-07 accept novelty 6.0 of 10

Explicit four-form fluxes in F-theory are constructed from algebraic cycles in the Weierstrass model, with D3 tadpoles and chirality indices computed and matched to type IIB in weak coupling.
F-theory GUTs with U(1) Symmetries: Generalities and Survey
hep-th 2011-02 conditional novelty 5.0 of 10

In F-theory SU(5) GUTs with a PQ symmetry, unification distortion and dimension-5 proton decay suppression are tied to the same integer, and a complete survey of two-U(1) spectral-cover models yields ten viable cases.

How the literature uses it

31 arXiv papers cite this in 52 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 30 sentences without a confident label

Builds on it 1 paper

In [ref] we have considerably extended this class of models by defining hypersurfaces in a subset of the toric ambient spaces described by the $473 800 776$ reflexive polyhedra in four dimensions [ref] .

Toric Methods in F-theory Model Building · Application to F-theory GUTs · 0.83

Uses its method or tool 2 papers

These intersection properties can be checked by performing an explicit resolution, employing compact toric methods in [ref] and the local methods and their extensions in [ref] .

Anomaly Cancellation And Abelian Gauge Symmetries In F-theory · F-theory as M-theory & the geometry of resolved fourfolds · 0.96
If the original four-fold $Y_4$ is realised as a hypersurface or complete intersection of a toric space, one can arrive at the same scaling relations and proper transform following the toric algorithm of [ref] as applied more recently to the resolution of Calabi-Yau four-folds in [ref] .

G_4 flux, chiral matter and singularity resolution in F-theory compactifications · U(1)-restricted Tate models and their resolution · 0.94

Uses its data or values 1 paper

For the $569 674$ extended weight systems discussed in [ref] we find only $27 345$ reflexive fourfold polytopes which have at least one nef partition.

Toric Methods in F-theory Model Building · Application to F-theory GUTs · 0.88

Compares with it 1 paper

Our results precisely match the toric resolution techniques applied to elliptic four-folds in [ref] .

G_4 flux, chiral matter and singularity resolution in F-theory compactifications · Summary and Outlook · 0.81

Cites it as background 13 papers

The geometric techniques that can be defined on complex manifolds enable us to build theories with rich phenomenology [ref] .

F-theory and the Witten Index · F-theory, D7-Branes Intersections and 8-dimensional SYM · 0.91
F-theory [ref] , has received a prominent role lately, due to the fact that GUTs can be consistently constructed and well founded, within F-theory's wide theoretical framework.

F-theory Yukawa Couplings and Supersymmetric Quantum Mechanics · Introduction · 0.97
Much work has been done on model building and phenomenology from both a local ( [ref] ) and global ( [ref] ) point of view.

Dirac gauginos and unification in F-theory · Introduction and Motivation · 1.00

What it cites · 65 sentences without a confident label

Uses the method or tool of 3 papers

Having reduced the number of interesting models by the constraints above we can explicitly construct F-theory GUTs using the prescription of [ref] .

Global F-theory GUTs · Introduction and Summary · 0.99
In our computer-based search for models we have made extensive use of the software package PALP [ref] .

math/0204356 · Introduction and Summary · 1.00
In this context the program cohomCalg [ref] may be helpful for the calculation of Hodge numbers.

Cohomology of Line Bundles: A Computational Algorithm · Conclusions · 0.94

Uses data or values from 1 paper

Instead of considering blowups of Fano threefolds, we pick a subset of $1088$ of the $473 800 776$ reflexive polyhedra in four dimensions [ref] .

Complete classification of reflexive polyhedra in four dimensions · Introduction and Summary · 0.96

Compares with 2 papers

Imposing the GUT groups on $S_5$ (first block) and $S_7$ (second block) we compute the following Hodge numbers: [equation] For the $SU(5)$ and $SU(10)$ model on $S_5$ the Euler numbers agree with the formula ([ref]) of [ref] , and there are also no further non-abelian enhancements in the Tate models.

Global F-theory GUTs · Three $dP_7$s · 0.99
In order to do so we will use a slightly different point of view than in [ref] : instead of classifying weight systems corresponding to blowups we will specify the ambient space by reflexive polyhedra in four dimensions.

Global SO(10) F-theory GUTs · Toric data for base manifolds · 0.86

Cites as background 19 papers

The class of global F-theory models, we aim to construct, have been first introduced in [ref] .

Global F-theory GUTs · Setup · 0.88
Starting with [ref] , F-theory has been recognized as a setup to elegantly construct Grand Unified Theories (GUTs) in string theory.

Model Building with F-Theory · Introduction and Summary · 1.00
Starting with [ref] , F-theory has been recognized as a setup to elegantly construct Grand Unified Theories (GUTs) in string theory.

GUTs and Exceptional Branes in F-theory - I · Introduction and Summary · 1.00

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