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Fitting fermion masses and mixings in F-theory GUTs
High Energy Physics - Theory · Submitted 15 Dec 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The relative simplicity of the model allows to perform the computation of Yukawa couplings for a region of its parameter space wider than previous attempts, obtaining realistic fermion masses and mixings for large parameter regions.
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The abstract, sentence by sentence
We analyse the structure of Yukawa couplings in local SU(5) F-theory models with $E_7$ enhancement. These models are the minimal setting in which the whole flavour structure for the MSSM charged fermions is encoded in a small region of the entire compactification space. In this setup the $E_7$ symmetry is broken down to SU(5) by means of a 7-brane T-brane background, and further to the MSSM gauge group by means of a hypercharge flux that also implements doublet-triplet splitting. At tree-level only one family of quarks and charged leptons is massive, while the other two obtain hierarchically smaller masses when stringy non-perturbative effects are taken into account. We find that there is a unique $E_7$ model with such hierarchical flavour structure. The relative simplicity of the model allows to perform the computation of Yukawa couplings for a region of its parameter space wider than previous attempts, obtaining realistic fermion masses and mixings for large parameter regions. Our results are also valid for local models with $E_8$ enhancement, pointing towards a universal structure to describe realistic fermion masses within this framework.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We analyse the structure of Yukawa couplings in local SU(5) F-theory models with $E_7$ enhancement. | contribution 0.98 | 0.92 | 0.04 | asserted 0.96 |
| s1 | These models are the minimal setting in which the whole flavour structure for the MSSM charged fermions is encoded in a small region of the entire compactification space. | background 0.97 | 0.20 | 0.05 | asserted 1.00 |
| s2 | In this setup the $E_7$ symmetry is broken down to SU(5) by means of a 7-brane T-brane background, and further to the MSSM gauge group by means of a hypercharge flux that also implements doublet-triplet splitting. | method 0.65 | 0.18 | 0.04 | asserted 1.00 |
| s3 | At tree-level only one family of quarks and charged leptons is massive, while the other two obtain hierarchically smaller masses when stringy non-perturbative effects are taken into account. | result 0.65 | 0.42 | 0.10 | asserted 1.00 |
| s4 | We find that there is a unique $E_7$ model with such hierarchical flavour structure. | result 1.00 | 0.96 | 0.52 | asserted 1.00 |
| s5 | The relative simplicity of the model allows to perform the computation of Yukawa couplings for a region of its parameter space wider than previous attempts, obtaining realistic fermion masses and mixings for large parameter regions. | result 0.58 | 0.96 | 0.36 | asserted 1.00 |
| s6 | Our results are also valid for local models with $E_8$ enhancement, pointing towards a universal structure to describe realistic fermion masses within this framework. | interpretation 0.97 | 0.78 | 0.21 | hedged possibility 0.67 |
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The paper
Original abstract
We analyse the structure of Yukawa couplings in local SU(5) F-theory models with $E_7$ enhancement. These models are the minimal setting in which the whole flavour structure for the MSSM charged fermions is encoded in a small region of the entire compactification space. In this setup the $E_7$ symmetry is broken down to SU(5) by means of a 7-brane T-brane background, and further to the MSSM gauge group by means of a hypercharge flux that also implements doublet-triplet splitting. At tree-level only one family of quarks and charged leptons is massive, while the other two obtain hierarchically smaller masses when stringy non-perturbative effects are taken into account. We find that there is a unique $E_7$ model with such hierarchical flavour structure. The relative simplicity of the model allows to perform the computation of Yukawa couplings for a region of its parameter space wider than previous attempts, obtaining realistic fermion masses and mixings for large parameter regions. Our results are also valid for local models with $E_8$ enhancement, pointing towards a universal structure to describe realistic fermion masses within this framework.
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References
How the literature uses it
14 arXiv papers cite this in 23 sentences
Papers citing it · 13 sentences without a confident label
Uses its method or tool 2 papers
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Once we understand these issues, we may be able to use the ultra-local approach developed in [ref] to computing Yukawa couplings within the intersecting region, but understanding those issues remains very challenging.
Applications of Flux Compactifications in F-Theory · Structure of Yukawa couplings · 0.93
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Once we understand these issues, we may be able to use the ultra-local approach developed in [ref] to computing Yukawa couplings within the intersecting region, but understanding those issues remains very challenging.
Towards natural and realistic $E_7$ GUTs in F-theory · Structure of Yukawa couplings · 0.90
Compares with it 2 papers
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Compared to previous work [ref] , the key ingredient to our approach is that contributions to the same couplings from different Yukawa points in the geometry are in general linearly independent.
Yukawa Hierarchies in Global F-theory Models · Conclusions and Outlook · 0.92
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The T-brane backgrounds that we considered in the previous section are very similar to those used to generate phenomenological Yukawa hierarchies in F-theory GUTs [ref] , with the main difference that there $Φ$ and $F$ are valued in the Lie algebra of the exceptional groups $E_6, E_7$ and $E_8$.
T-branes and $\alpha'$-corrections · Applications to local F-theory models · 0.91
Cites it as background 6 papers
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T-branes [ref] can be seen as bound states of ordinary D-branes, characterized by non-commuting vev's for two of their worldvolume scalars.[Further readings on the subject of T-branes include [ref] .] In the present context, we consider T-branes made from stacks of non-perturbative 7-branes (or of ordinary D6-branes for the 3d case).
SUSY enhancement from T-branes · Introduction · 0.98
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They were first introduced in [ref] , and have since received a fair bit of interest, with reasons ranging from their fundamental structure to the attractiveness of their low-energy features for model-building in string phenomenology [ref] .
T-branes and Matrix Models · Introduction · 1.00
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Since then, there has been a lot of effort to understand these BPS objects and their rôle in string compactifications [ref] .
T-branes and defects · Introduction · 1.00
What it cites · 107 sentences without a confident label
Uses the method or tool of 15 papers
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For this we will follow the scheme in [ref] (see also [ref] ) in which rank one Yukawa matrices are obtained at tree-level and then enhanced to rank three when external non-perturbative effects (like Euclidean D3-brane instantons) are taken into account.[For other approaches to the generation of Yukawa hierarchies in F-theory GUTs see e.g. [ref] .]
Yukawa Structure from U(1) Fluxes in F-theory Grand Unification · Introduction · 0.98
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For this we will follow the scheme in [ref] (see also [ref] ) in which rank one Yukawa matrices are obtained at tree-level and then enhanced to rank three when external non-perturbative effects (like Euclidean D3-brane instantons) are taken into account.[For other approaches to the generation of Yukawa hierarchies in F-theory GUTs see e.g. [ref] .]
Flux and Instanton Effects in Local F-theory Models and Hierarchical Fermion Masses · Introduction · 0.98
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For this we will follow the scheme in [ref] (see also [ref] ) in which rank one Yukawa matrices are obtained at tree-level and then enhanced to rank three when external non-perturbative effects (like Euclidean D3-brane instantons) are taken into account.[For other approaches to the generation of Yukawa hierarchies in F-theory GUTs see e.g. [ref] .]
Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) Unification · Introduction · 0.98
Uses data or values from 1 paper
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We show in table [ref] the extrapolation of the fermion masses up to the unification scale taken from [ref] in the context of the MSSM.
Unification and Fermion Mass Structure · Fitting fermion masses and mixing angles · 0.95
Compares with 6 papers
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Interestingly, we obtain that such model contains the same structure of matter curves and Yukawa couplings as the $E_8$ model selected in [ref] through the same criteria of realistic fermion mass spectrum.
Yukawa hierarchies at the point of $E_8$ in F-theory · Introduction · 1.00
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In particular we see that the present model is more general, and that we recover the same matter curves as in [ref] if we set $a=b$.[The precise dictionary connecting the two models would be -(1+2d) μ^2 μ_2^2 -2dκ κwhere the parameters in the left hand side of [ref] are the ones appearing in [ref] and the parameters in the right hand side are the ones of this paper. ] However, as we will see below considering $a ≠b$ will be crucial in order to implement the doublet-triplet splitting mechanism of [ref] and it will also greatly increase the region of parameters for which we can reproduce the empirical masses and mixing for charged MSSM fermions.
GUTs and Exceptional Branes in F-theory - II: Experimental Predictions · Holomorphic gauge · 0.88
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Since these Yukawas are essentially the same ones as found in the context of local $E_8$ models in [ref] , our results point towards some sort of universal structure for realistic Yukawas in the context of the proposal made in [ref] .
Non-perturbative effects on seven-brane Yukawa couplings · Conclusions · 0.85
Cites as support 2 papers
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This fact is illustrated by the recent analysis in [ref] , which showed that out of several initial local models with similar features most of them could be discarded at the level of the holomorphic Yukawa couplings.
Yukawa hierarchies at the point of $E_8$ in F-theory · Introduction · 0.99
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As shown in [ref] this does not affect the computation of holomorphic Yukawa couplings and so we may safely ignore this background shift in the discussion below.
Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) Unification · Residue formula for Yukawa couplings · 0.96
Cites as background 6 papers
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A key pledge of F-theory GUT models [ref] is to provide a UV complete framework where gauge coupling unification and realistic Yukawa couplings occur at the same time.
Breaking GUT Groups in F-Theory · Introduction · 0.90
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A key pledge of F-theory GUT models [ref] is to provide a UV complete framework where gauge coupling unification and realistic Yukawa couplings occur at the same time.
GUTs and Exceptional Branes in F-theory - I · Introduction · 0.90
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A key pledge of F-theory GUT models [ref] is to provide a UV complete framework where gauge coupling unification and realistic Yukawa couplings occur at the same time.
GUTs and Exceptional Branes in F-theory - II: Experimental Predictions · Introduction · 0.90
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