{"arxiv_id":"1204.3247","incoming":{"papers":3,"sentences":7,"groups":[{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1411.6696","title":"Moduli in General $SU(3)$-Structure Heterotic Compactifications","url":"/paper/1411.6696","section":"Four-Dimensional Domain Walls","sentence":"As we shall see, the zeroth order solution is not sufficient to stabilise the geometric moduli of the internal space $X_6$, as has been pointed out before [ref] .","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":6},"outgoing":{"papers":59,"sentences":85,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":6,"sentences":6,"quotes":[{"arxiv_id":"math/0202282","title":"The intrinsic torsion of SU(3) and G_2 structures","url":"/paper/math/0202282","section":"Motivations and outline","sentence":"This question will be answered using the $G$-structure formalism [ref] applied to the heterotic case for the groups $G_2$ and $SU(3)$.","intent_p":0.97,"contests_p":null},{"arxiv_id":"hep-th/0211118","title":"Non-Kaehler String Backgrounds and their Five Torsion Classes","url":"/paper/hep-th/0211118","section":"Motivations and outline","sentence":"This question will be answered using the $G$-structure formalism [ref] applied to the heterotic case for the groups $G_2$ and $SU(3)$.","intent_p":0.97,"contests_p":null},{"arxiv_id":"math/0107101","title":"Stable forms and special metrics","url":"/paper/math/0107101","section":"Motivations and outline","sentence":"This question will be answered using the $G$-structure formalism [ref] applied to the heterotic case for the groups $G_2$ and $SU(3)$.","intent_p":0.97,"contests_p":null},{"arxiv_id":"hep-th/0205050","title":"G-Structures and Wrapped NS5-Branes","url":"/paper/hep-th/0205050","section":"The ten-dimensional solution","sentence":"With the definitions [ref] of the $G_2$ structure forms $φ$ and $$, this leads to the following set of equations [equation] We can further contract them with the basis of the co-tangent space to obtain differential forms [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"math/0112201","title":"Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds","url":"/paper/math/0112201","section":"The ten-dimensional solution","sentence":"With the definitions [ref] of the $G_2$ structure forms $φ$ and $$, this leads to the following set of equations [equation] We can further contract them with the basis of the co-tangent space to obtain differential forms [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":3,"sentences":3,"quotes":[{"arxiv_id":"0905.1334","title":"Domain wall flow equations and SU(3)xSU(3) structure compactifications","url":"/paper/0905.1334","section":"Comparison between ten and four dimensions","sentence":"We would like to show that the four-dimensional domain wall [ref] indeed matches our $10$-dimensional solution [ref] in a way similar to what happens in the context of type IIA [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"hep-th/0407198","title":"Domain Walls, Hitchin's Flow Equations and G_2-Manifolds","url":"/paper/hep-th/0407198","section":"Comparison between ten and four dimensions","sentence":"We would like to show that the four-dimensional domain wall [ref] indeed matches our $10$-dimensional solution [ref] in a way similar to what happens in the context of type IIA [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"hep-th/0211102","title":"Mirror Symmetry in Generalized Calabi-Yau Compactifications","url":"/paper/hep-th/0211102","section":"$G_2/SU(3)$","sentence":"This is analogous to the original type II mirror symmetry correspondence with NS-NS flux [ref] .","intent_p":0.9,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":15,"sentences":17,"quotes":[{"arxiv_id":"0709.1932","title":"Heterotic String Compactifications on Half-flat Manifolds II","url":"/paper/0709.1932","section":"Mirror half-flat manifolds","sentence":"Heterotic compactifications on half-flat mirror manifolds have been studied in Refs. [ref] and, here, we briefly review the main results.","intent_p":0.93,"contests_p":null},{"arxiv_id":"hep-th/0408121","title":"Heterotic on Half-flat","url":"/paper/hep-th/0408121","section":"Mirror half-flat manifolds","sentence":"Heterotic compactifications on half-flat mirror manifolds have been studied in Refs. [ref] and, here, we briefly review the main results.","intent_p":0.93,"contests_p":null},{"arxiv_id":"hep-th/0304126","title":"Anomaly, Fluxes and (2,0) Heterotic-String Compactifications","url":"/paper/hep-th/0304126","section":"Killing spinor equations and Bianchi identity","sentence":"This would be the basis for finding in subsequent work a complete solution perturbatively at all orders, see Refs. [ref] for a general discussion of the $α'$ expansion.","intent_p":0.95,"contests_p":null},{"arxiv_id":"1010.4031","title":"Non-Kahler heterotic rotations","url":"/paper/1010.4031","section":"Killing spinor equations and Bianchi identity","sentence":"This would be the basis for finding in subsequent work a complete solution perturbatively at all orders, see Refs. [ref] for a general discussion of the $α'$ expansion.","intent_p":0.95,"contests_p":null},{"arxiv_id":"math/0606705","title":"The Srni lectures on non-integrable geometries with torsion","url":"/paper/math/0606705","section":"$G$-structures and torsion classes","sentence":"More details can be found in the literature, e.g. in Refs. [ref] .","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":59},"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. 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