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F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds
High Energy Physics - Theory · Submitted 18 Dec 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We present compact three-generation F-theory GUT models meeting in particular the constraints of D3-tadpole cancellation and D-term supersymmetry.
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We present compact three-generation F-theory GUT models meeting in particular the constraints of D3-tadpole cancellation and D-term supersymmetry. To this end we explicitly construct elliptically fibered Calabi-Yau fourfolds as complete intersections in a toric ambient space. Toric methods enable us to control the singular geometry of the SU(5) GUT model. The GUT brane wraps a non-generic del Pezzo surface admitting GUT symmetry breaking via hypercharge flux. It is contractible to a curve and we demonstrate the existence of a consistent decoupling limit. We compute the Euler characteristic of the singular Calabi-Yau fourfold to show that our three-generation flux solutions obtained via the spectral cover construction are consistent with D3-tadpole cancellation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present compact three-generation F-theory GUT models meeting in particular the constraints of D3-tadpole cancellation and D-term supersymmetry. | contribution 0.96 | 0.95 | 0.75 | asserted 1.00 |
| s1 | To this end we explicitly construct elliptically fibered Calabi-Yau fourfolds as complete intersections in a toric ambient space. | method 0.92 | 0.95 | 0.06 | asserted 1.00 |
| s2 | Toric methods enable us to control the singular geometry of the SU(5) GUT model. | method 0.93 | 0.66 | 0.04 | asserted 1.00 |
| s3 | The GUT brane wraps a non-generic del Pezzo surface admitting GUT symmetry breaking via hypercharge flux. | contribution 0.64 | 0.78 | 0.10 | asserted 1.00 |
| s4 | It is contractible to a curve and we demonstrate the existence of a consistent decoupling limit. | result 0.79 | 0.91 | 0.08 | asserted 1.00 |
| s5 | We compute the Euler characteristic of the singular Calabi-Yau fourfold to show that our three-generation flux solutions obtained via the spectral cover construction are consistent with D3-tadpole cancellation. | result 0.81 | 0.96 | 0.28 | asserted 0.94 |
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The paper
Original abstract
We present compact three-generation F-theory GUT models meeting in particular the constraints of D3-tadpole cancellation and D-term supersymmetry. To this end we explicitly construct elliptically fibered Calabi-Yau fourfolds as complete intersections in a toric ambient space. Toric methods enable us to control the singular geometry of the SU(5) GUT model. The GUT brane wraps a non-generic del Pezzo surface admitting GUT symmetry breaking via hypercharge flux. It is contractible to a curve and we demonstrate the existence of a consistent decoupling limit. We compute the Euler characteristic of the singular Calabi-Yau fourfold to show that our three-generation flux solutions obtained via the spectral cover construction are consistent with D3-tadpole cancellation.
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References
How the literature uses it
68 arXiv papers cite this in 137 sentences
Papers citing it · 79 sentences without a confident label
Builds on it 2 papers
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Therefore, the proposal is that we first break $E_7$ down to an intermediate $(5)$ with vertical flux, then obtain $$ using hypercharge flux, in parallel with earlier work on tuned SU(5) GUT models [ref] .
Applications of Flux Compactifications in F-Theory · Standard Model chiral matter · 0.81
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[ref] and show that the mirror is again elliptically fibered.
On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs · Split spectal covers and mirror symmetry for $U(1)$-restricted Tate models · 0.91
Uses its method or tool 7 papers
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Following [ref] we will blow up points and curves inside the Fano threefolds until the requirements for a GUT model are satisfied.
Global SO(10) F-theory GUTs · General idea · 0.81
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The gauge theory will be $SU(5)$ and $SU(5) ×U(1)$ and we perform an explicit resolution of all co-dimension singularities as in [ref] by modifying the toric ambient space.
F-theory fluxes, Chirality and Chern-Simons theories · Introduction · 0.97
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A useful indirect procedure to determine such components has been established, through the matching of Chern-Simons (CS) terms in M/F-theory duality [ref] .
Applications of Flux Compactifications in F-Theory · Chiral matter and matter surfaces · 0.96
Compares with it 2 papers
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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
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The model in [ref] has a more involved structure, but similar qualitative features.
Discrete gauge symmetries in D-brane models · Discrete gauge symmetries in local F-theory GUTs · 0.91
Cites it as support 3 papers
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We assume here that these local constructions can be embedded in a global compactification such that the hypercharge remains massless, as has been shown in explicit global realizations [ref] .
Rational F-Theory GUTs without exotics · Introduction and summary of results · 0.99
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In fact, this is the case for the explicit elliptically fibered Calabi-Yau fourfolds used for GUT model-building given by two constraints [ref] , as well as the elliptically fibered Calabi-Yau hypersurfaces studied in [ref] .
On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs · Mirror symmetry and spectral covers · 0.97
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Such realizations allow for more exhaustive choices of fluxes on the GUT brane as demonstrated in the models of [ref] .
Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors · The Polytope of Compactifications · 0.99
Cites it as background 37 papers
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Global F-theory GUT models have been first constructed in [ref] .
Global SO(10) F-theory GUTs · Introduction · 0.89
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The full set of resolutions of the SU(5) model admitting a holomorphic zero section were worked out in [ref] (see also [ref] ) and the chiral indices were computed for a subset of these resolutions in [ref] using similar methods to those described in this paper, as well as by other methods in e.g. [ref] .
Chiral matter multiplicities and resolution-independent structure in 4D F-theory models · $(5)$ model · 0.89
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Most of the work on these models has focused on the GUT group of $(5)$ and its $(1)$ extensions [ref] , while there has also been some study of $(10)$ GUTs [ref] .
Applications of Flux Compactifications in F-Theory · Introduction · 0.91
What it cites · 97 sentences without a confident label
Builds on 1 paper
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To remedy this problem, we generalise the geometries of [ref] to an entire sequence of torically constructed Calabi-Yau fourfolds.
Global F-theory GUTs · Introduction · 1.00
Uses the method or tool of 9 papers
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It is not hard to check that the splits of $∇$ into $(∇_1,∇_2)$ determine a valid nef-partition.[This can be done by using the program PALP [ref] .] Since $∇_1$ contains the points $(ν_1,ν_2,ν_3)$ corresponding to the coordinates $(x,y,z)$ of the elliptic fiber one checks using [ref] that $p_1 ≡P_W=0$ is precisely the Tate form [ref].
math/0204356 · On the toric construction of elliptic fourfolds · 1.00
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E.g. the computation of the relevant Euler characteristic, either directly [ref] or via the method proposed for a certain class of geometries in [ref] , requires explicit control of the singularities of $Y$.
Global F-theory GUTs · Calabi-Yau fourfolds in toric ambient spaces · 0.83
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E.g. the computation of the relevant Euler characteristic, either directly [ref] or via the method proposed for a certain class of geometries in [ref] , requires explicit control of the singularities of $Y$.
From Local to Global in F-Theory Model Building · Calabi-Yau fourfolds in toric ambient spaces · 0.83
Uses data or values from 1 paper
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Here we merely list the final results from [ref] in terms of the above parametrisation of the spectral cover line bundle,
Global F-theory GUTs · Gauge flux from spectral cover bundles · 0.82
Compares with 1 paper
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In the compact examples of the type discussed in [ref] and in this article, by contrast, $S$ is a non-generic del Pezzo surface and is only contractible to a curve.
Global F-theory GUTs · Decoupling Limit · 0.87
Cites as support 1 paper
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Indeed, the above choice guarantees that $c_1(V) + c_1(L) =0$ [ref] .
Global F-theory GUTs · Gauge flux from spectral cover bundles · 0.97
Cites as background 36 papers
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It is interpreted as the result of breaking the maximal $E_8$ enhancement of the $ℙ_1,2,3[6]$ fiber by a non-trivial Higgs bundle [ref] with structure group $H$ over $S$.
GUTs and Exceptional Branes in F-theory - I · Spectral covers for $SU(5)$ models · 0.87
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It is interpreted as the result of breaking the maximal $E_8$ enhancement of the $ℙ_1,2,3[6]$ fiber by a non-trivial Higgs bundle [ref] with structure group $H$ over $S$.
Model Building with F-Theory · Spectral covers for $SU(5)$ models · 0.87
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The explicit construction of compact $SU(5)$ GUT vacua with hypercharge induced GUT symmetry breaking [ref] was initiated in [ref] actually not in fully fledged F-theory, but, as a first step, in the framework of Type IIB orientifolds within the well-defined framework of toric geometry.
GUTs and Exceptional Branes in F-theory - II: Experimental Predictions · Introduction · 0.86
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