{"arxiv_id":"1007.1297","incoming":{"papers":60,"sentences":129,"groups":[{"kind":"extends","label":"Builds on it","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1406.6290","title":"Discrete Family Symmetry from F-Theory GUTs","url":"/paper/1406.6290","section":"$S_3$ and $Z_3$ models for $(3,1,1)$ factorisation","sentence":"As already stated, if no other conditions are imposed on $a_k$ this model is considered as an $S_3$ variant of the $3+1+1$ example given in [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"1205.6930","title":"Building SO(10) models from F-theory","url":"/paper/1205.6930","section":"First example","sentence":"Remarkably, this model is the $SO(10)$ upgrade of the $3+1+1+1$ example given in [ref] .","intent_p":0.91,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":5,"sentences":7,"quotes":[{"arxiv_id":"1203.4490","title":"Wavefunctions and the Point of E8 in F-theory","url":"/paper/1203.4490","section":"Semi-local constraints on matter spectrum","sentence":"Following precisely the methodology and notation of [ref] we start from a fully split spectral cover C_10 = (a_1 V + a_6 U ) (a_2 V + a_7 U ) (a_3 V + a_8 U) (a_4 V + a_9 U) (a_5 V + a_10 U) = 0 .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1604.01669","title":"MSSM-like from $SU_{5}\\times D_{4}$ Models","url":"/paper/1604.01669","section":"Abelian monodromy","sentence":"Using the method of [ref] , the possible abelian monodromies are $ℤ_2$, $ℤ_3$, $ℤ_4,$ $ℤ_2×ℤ_3$ and $ℤ_2×ℤ_2$; they lead to factorizations of the $𝒞_5$ spectral cover as [equation] and to the respective identification of the weights ${ t_1,t_2}$, ${ t_1,t_2,t_3}$, ${ t_1,t_2,t_3,t_4}$, ${ t_1,t_2} ∪{ t_3,t_4,t_5}$ and ${ t_1,t_2} ∪{ t_3,t_4}$.The algebraic equations for the matter curves $Σ_t_i$, $Σ_t_i+t_j$, $Σ_t_i-t_j$ in terms of the $t_i$ weights associated with the $SU_5^⊥$ fundamental representation are respectively given by $t_i=0$; $( t_i+t_j) _i<j=0$ and $±( t_i-t_j) _i<j=0$; they are denoted like $10_t_i,$ $5̅_t_i+t_j$ and $1_±( t_i-t_j)$; see eq(<ref>).","intent_p":0.91,"contests_p":null},{"arxiv_id":"1505.00937","title":"Phenomenological implications of a minimal F-theory GUT with discrete symmetry","url":"/paper/1505.00937","section":"The discrete group $D_4$ as a Family Symmetry","sentence":"These are readily determined from the known Chern classes of the $b_k$ coefficients through the equations $b_k=b_k(a_i)$ given in ([ref]), using well known procedures [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"1203.6277","title":"Aspects of F-Theory GUTs","url":"/paper/1203.6277","section":"The case of $Z_2$ monodromy","sentence":"We make the Ansatz [ref] [equation] Substituting into $b_n$'s we get b_0 = c a_5^2 a_7^2 a_9^2 b_2 = a_1 a_5 a_7 a_9-(a_5^2 a_7^2 a_8^2+a_5 a_7 (a_5 a_6+a_4 a_7) a_9 a_8+(a_5^2 a_6^2+a_4 a_5 a_7 a_6+a_4^2 a_7^2) a_9^2) c b_3 = a_1 (a_5 a_7 a_8+a_5 a_6 a_9+a_4 a_7 a_9)-(a_5 a_6+a_4 a_7) (a_5 a_8+a_4 a_9) (a_7 a_8+a_6 a_9) c b_4 = a_1 (a_5 a_6 a_8+a_4 a_7 a_8+a_4 a_6 a_9)-a_4 a_6 a_8 (a_5 a_7 a_8+a_5 a_6 a_9+a_4 a_7 a_9) c b_5 = a_1 a_4 a_6 a_8Next, we observe that we have to determine the homology classes $[a_i]$ of nine unknowns $a_1,…a_9$ in terms of the $b_k$-classes $[b_k]$.","intent_p":0.85,"contests_p":null},{"arxiv_id":"1205.6930","title":"Building SO(10) models from F-theory","url":"/paper/1205.6930","section":"$SU(5)$ spectrum","sentence":"The case of $Z_2$ monodromy corresponds to the following splitting of the spectral cover equation b_0∏_i(s-t_i)=(a_1+a_2s+a_3s^2)(a_4+a_5s)(a_6+a_7s)(a_8+a_9s)=∑_k=0^5 b_k s^5-k Following [ref] we derive the relations of $b_k(a_i)$ by equating coefficients of the same powers in $s$, while we use a suitable Ansatz for $a_i$'s to solve the constraint $b_1(a_i)=0$.","intent_p":0.87,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1308.1581","title":"Neutrino mass textures from F-theory","url":"/paper/1308.1581","section":"$SU(5)$ spectrum","sentence":"The third column shows the homology classes of the matter curves computed in [ref] .","intent_p":0.8,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1209.4421","title":"A Note on Hypercharge Flux, Anomalies, and U(1)s in F-theory GUTs","url":"/paper/1209.4421","section":"GUT Anomalies and the Local Geometry","sentence":"Unlike the constraints ([ref]) and ([ref]), the constraint ([ref]) does not come out from the type of local geometry or spectral cover analysis presented in [ref] for example.","intent_p":0.81,"contests_p":null},{"arxiv_id":"1205.6930","title":"Building SO(10) models from F-theory","url":"/paper/1205.6930","section":"A $Z_2$ matter parity for a model with $2+3$ spectral cover split","sentence":"Notice that the latter does not coincide with the parity chosen in [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"1009.6000","title":"Yukawa couplings and fermion mass structure in F-theory GUTs","url":"/paper/1009.6000","section":"A simple model for doublet-triplet splitting","sentence":"This is in contrast to the example given in [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1303.5054","title":"Elliptic fibrations for SU(5) x U(1) x U(1) F-theory vacua","url":"/paper/1303.5054","section":"An SU(5)xU(1)2 model","sentence":"It is interesting to note that these charges can be accommodated in a local 2-2-1 split spectral cover model as constructed in [ref] .","intent_p":0.83,"contests_p":null},{"arxiv_id":"1306.0577","title":"Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors","url":"/paper/1306.0577","section":"Different Splits and the Fundamental Representation","sentence":"Finally, let us point out that the above notion of splits agrees with the cases that have been analyzed with the split spectral cover constructions [ref] only in the case of a single $U(1)$.","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":21,"sentences":24,"quotes":[{"arxiv_id":"1102.5244","title":"Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs","url":"/paper/1102.5244","section":"Application to a realistic minimal model","sentence":"To start with, we recall here the basic features of the model [ref] which emerges from the general class [ref] presented in Table [ref].","intent_p":0.83,"contests_p":null},{"arxiv_id":"1512.09148","title":"MSSM from F-theory SU(5) with Klein Monodromy","url":"/paper/1512.09148","section":"Analysis of the $Z_2×Z_2$ model","sentence":"To set the stage, we first present a short review of the basic characteristics of the model following mainly the notation of [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"1402.4096","title":"Hypercharge flux in F-theory and the stable Sen limit","url":"/paper/1402.4096","section":"Introduction","sentence":"This phenomenon was discovered in [ref] in IIB string theory (see also [ref] ), and was propagated to F-theory in [ref] (see [ref] for a review).","intent_p":0.9,"contests_p":null},{"arxiv_id":"1008.2506","title":"On Global Flipped SU(5) GUTs in F-theory","url":"/paper/1008.2506","section":"Introduction","sentence":"The semi-local and global $SU(5)$ GUTs in F-theory have been discussed in [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1406.6290","title":"Discrete Family Symmetry from F-Theory GUTs","url":"/paper/1406.6290","section":"The $C_3×C_2$ spectral cover split","sentence":"The details concerning the spectrum, homologies and flux restrictions of this model can be found in [ref] .","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":90},"outgoing":{"papers":48,"sentences":116,"groups":[{"kind":"data_used","label":"Uses data or values 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.","intent_p":0.96,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":2,"sentences":3,"quotes":[{"arxiv_id":"0912.0853","title":"Froggatt-Nielsen models from E8 in F-theory GUTs","url":"/paper/0912.0853","section":"Froggatt-Nielsen and quark-lepton mass splitting","sentence":"As shown in [ref] 3-curve models can recreate realistic quark and lepton mixing at the GUT level.","intent_p":0.96,"contests_p":null},{"arxiv_id":"1005.1025","title":"Family symmetries in F-theory GUTs","url":"/paper/1005.1025","section":"Introduction","sentence":"The second is that it is possible to realise the idea that each MSSM generation comes from a different matter curve which as shown in [ref] can lead to attractive models of flavour.","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":27,"sentences":38,"quotes":[{"arxiv_id":"1001.0577","title":"Particle Physics Implications of 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string GUT constructions have been developed in the context of F-theory [ref] (see [ref] for a phenomenological review).","intent_p":1.0,"contests_p":null},{"arxiv_id":"0802.3391","title":"GUTs and Exceptional Branes in F-theory - I","url":"/paper/0802.3391","section":"Introduction","sentence":"Recently string GUT constructions have been developed in the context of F-theory [ref] (see [ref] for a phenomenological review).","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":72},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. 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A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"3 later papers by other authors are listed below: 3 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/1007.1297"}}