{"arxiv_id":"1303.6727","incoming":{"papers":50,"sentences":88,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1509.06973","title":"Towards Weakly Constrained Double Field Theory","url":"/paper/1509.06973","section":"Conclusion","sentence":"One can easily deduce that the double-vielbein formalism in strongly constrained DFT [ref] would be easily generalized to the weakly constrained DFT case through the $∘$-product.","intent_p":0.95,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1402.5027","title":"U-gravity : ${\\mathbf{SL}(N)}$","url":"/paper/1402.5027","section":"Introduction","sentence":"While the motivation of our work comes from the Dynkin diagram prediction [ref] and the $E_11$ proposal [ref] , for the actual construction of the $$ U-gravity, we heavily employ the differential geometry tools from [ref] which were developed to provide an underlying `stringy' differential geometry for DFT (see Table [ref] for its characteristic).[Alternative approaches include [ref] .] The methods have been successfully applied to construct Yang-Mills DFT [ref] , coupling to fermions [ref] , coupling to RR-sector [ref] , $=1, D=10$ (full order) super DFT [ref] , $=2, D=10$ (full order) super DFT [ref] , and the completely covariant string action on doubled-yet-gauged spacetime [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1605.00385","title":"A geometric formulation of exceptional field theory","url":"/paper/1605.00385","section":"Scalar potential","sentence":"We will use a Weitzenböck-like connection [equation] and derive $V_1$ in terms of the generalised torsion of this connection, mirroring the construction in [ref] .[This is related to the flux formulation of DFT and EFT but is different to the construction used in [ref] .] The generalised torsion is defined as [equation] where $_ab$ is an irrep of the generalised torsion.","intent_p":0.8,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1705.08181","title":"Duality Twisted Reductions of Double Field Theory of Type II Strings","url":"/paper/1705.08181","section":"Introduction","sentence":"We should also note that, the results of [ref] was also obtained by [ref] , by considering the duality twisted reductions of the DFT action they constructed in terms of a torsionful, flat generalized connection, called the Weitzenböck connection[This formulation of the DFT action has the added advantage that it already includes an extra term, which has to be added by hand in the original formulation.","intent_p":0.84,"contests_p":null},{"arxiv_id":"1412.0635","title":"Geometry and fluxes of SL(5) exceptional field theory","url":"/paper/1412.0635","section":"Constructing the action","sentence":"This is exactly as expected from the double field theory case, where the Lagrangian resulting from requiring invariance under generalised Lorentz transformations led exactly to the analogous term needed for gauged double field theory [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1707.00714","title":"Half-maximal supersymmetry from exceptional field theory","url":"/paper/1707.00714","section":"Reformulating double field theory","sentence":"This is analogous to [ref] where the scalar potential was rewritten in terms of the Weitzenböck torsion by requiring invariance under local $d ×d$ or $5$ transformations, in the case of DFT and $5$ EFT, respectively.","intent_p":0.83,"contests_p":null},{"arxiv_id":"1605.00385","title":"A geometric formulation of exceptional field theory","url":"/paper/1605.00385","section":"Comparison to standard and gauged EFT","sentence":"Nonetheless, in gauged EFT one also finds that the section condition can be relaxed, see for example the analogous discussion for gauged DFT [ref] and also the review [ref] : for closure of the algebra one must impose the quadratic constraint on the embedding tensor, which by [ref] automatically satisfies the linear constraint, and the section condition [ref], where in this case the background vielbeine would be $W_ab$, [ref].","intent_p":0.92,"contests_p":null},{"arxiv_id":"1505.01301","title":"Supersymmetric gauged Double Field Theory: Systematic derivation by virtue of \\textit{Twist}","url":"/paper/1505.01301","section":"Properties of the U-derivative and its connection","sentence":"It is also worth while to compare with the Weitzenböck connection, e.g. [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":24,"sentences":30,"quotes":[{"arxiv_id":"1710.09740","title":"Exotic branes in Exceptional Field Theory: the SL(5) duality group","url":"/paper/1710.09740","section":"Introduction","sentence":"The role of the Weitzenböck connection and the generalised torsion in exceptional field theories was first discussed in [ref] and later for DFT in [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"1807.08443","title":"Kerr-Schild Double Field Theory and Classical Double Copy","url":"/paper/1807.08443","section":"Introduction","sentence":"It provides a unified geometric framework for the entire closed string massless NS-NS sector encoded in DFT field variables [ref] : the generalized metric $ℋ_MN$ and the DFT dilaton $d$.","intent_p":0.88,"contests_p":null},{"arxiv_id":"1904.11650","title":"Heterotic Kerr-Schild Double Field Theory and Classical Double Copy","url":"/paper/1904.11650","section":"Introduction","sentence":"Double field theory (DFT) [ref] is a low energy effective field theory of strings with manifest $𝑂(d,d)$ T-duality [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1608.04734","title":"Black hole thermodynamics, stringy dualities and double field theory","url":"/paper/1608.04734","section":"On curvature, singularities and horizons","sentence":"The geometry of double field theory is based on generalised diffeomorphisms, as defined in [ref], and hence is not that of conventional differential geometry [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"1412.8769","title":"Exotic branes and non-geometric fluxes","url":"/paper/1412.8769","section":"$β$-supergravity","sentence":"In the special case of $T$-folds, we can globally describe the backgrounds within a framework of the double field theory (DFT), which is a $T$-duality covariant reformulation of the low-energy supergravity theory [ref] .","intent_p":0.8,"contests_p":null}]}],"unlabelled_sentences":50},"outgoing":{"papers":50,"sentences":109,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1109.0290","title":"The effective action of Double Field Theory","url":"/paper/1109.0290","section":"Discussion","sentence":"We do this by an analogue of the Scherk-Schwarz mechanism applicable to generalised geometry [ref] 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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. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1303.6727"}}