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Non-simply-laced Lie algebras via F theory strings
High Energy Physics - Theory · Submitted 27 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We give an explicit description of the folding of D_{2n} to B_n of the folding of E_6 to F_4 and that of D_4 to G_2 in terms of junctions and Jordan strings.
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The abstract, sentence by sentence
In order to describe the appearance in F theory of the non--simply--laced Lie algebras, we use the representation of symmetry enhancements by means of string junctions. After an introduction to the techniques used to describe symmetry enhancement, that is algebraic geometry, BPS states analysis and string junctions, we concentrate on the latter. We give an explicit description of the folding of D_{2n} to B_n of the folding of E_6 to F_4 and that of D_4 to G_2 in terms of junctions and Jordan strings. We also discuss the case of C_n, but we are unable in this case to provide a string interpretation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In order to describe the appearance in F theory of the non--simply--laced Lie algebras, we use the representation of symmetry enhancements by means of string junctions. | method 0.75 | 0.78 | 0.23 | asserted 0.99 |
| s1 | After an introduction to the techniques used to describe symmetry enhancement, that is algebraic geometry, BPS states analysis and string junctions, we concentrate on the latter. | background 0.74 | 0.54 | 0.04 | asserted 0.89 |
| s2 | We give an explicit description of the folding of D_{2n} to B_n of the folding of E_6 to F_4 and that of D_4 to G_2 in terms of junctions and Jordan strings. | contribution 0.77 | 0.93 | 0.42 | asserted 1.00 |
| s3 | We also discuss the case of C_n, but we are unable in this case to provide a string interpretation. | limitation 1.00 | 0.90 | 0.05 | asserted 0.96 |
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Original abstract
In order to describe the appearance in F theory of the non--simply--laced Lie algebras, we use the representation of symmetry enhancements by means of string junctions. After an introduction to the techniques used to describe symmetry enhancement, that is algebraic geometry, BPS states analysis and string junctions, we concentrate on the latter. We give an explicit description of the folding of D_{2n} to B_n of the folding of E_6 to F_4 and that of D_4 to G_2 in terms of junctions and Jordan strings. We also discuss the case of C_n, but we are unable in this case to provide a string interpretation.
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References
How the literature uses it
14 arXiv papers cite this in 18 sentences
Papers citing it · 11 sentences without a confident label
Compares with it 1 paper
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The basis we determine for these deformations differs from the canonical basis and makes the $_3$ automorphism more transparent; a similar computation was performed in the canonical basis in [ref] , though the results were not derived directly from a deformed geometry.
Matter From Geometry Without Resolution · Introduction · 0.99
Cites it as background 5 papers
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For earlier work on the use of string junctions and its relation to symmetries realized on a 7-brane, see e.g. references [ref] .
S-folds, String Junctions, and 4D $\mathcal{N} = 2$ SCFTs · Introduction · 0.97
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Some aspects of this case are discussed in [ref] .
T-Branes, String Junctions, and 6D SCFTs · Nilpotent Orbits from String Junctions · 0.85
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Recent works have made significant progress in understanding the physics of F-theory compactifications, including globally consistent models [ref] , $U(1)$ symmetries [ref] , instanton corrections [ref] , the physics of codimension two and three singularities [ref] , and chirality inducing $G_4$-flux [ref] ; there has also been progress in understanding the landscape of six-dimensional F-theory compactifications [ref] .
Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory · Introduction · 0.99
What it cites · 24 sentences without a confident label
Uses the method or tool of 1 paper
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For practical reasons we avoid introducing new notation and adopt that of [ref] .
String Junctions for Arbitrary Lie Algebra Representations · String junctions · 0.90
Cites as background 5 papers
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While the full classification of symmetry enhancements can be found in [ref] , let us write here the polynomials whose factorization distinguishes the split case from the non-split one, also in the other branches of the algorithm, which are relevant for us because they contain the orthogonal and the exceptional gauge symmetries.
Geometric Singularities and Enhanced Gauge Symmetries · Geometric perspective · 0.81
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[ref] in the first scheme referred to above, that is when F theory is compactified on $R_1,7 ×K3$.
BPS Open Strings and A-D-E-singularities in F-theory on K3 · String perspective · 0.90
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The recent return of interest in F theory, [ref] , has originated from the suggestion of possible low energy phenomenological implications, more precisely by the possibility to accommodate in this theory a gravity decoupling at the scale of grand-unification together with low energy effective grand-unified actions which extend the MSSM, [ref] .
Model Building with F-Theory · Introduction · 0.94
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