{"arxiv_id":"0712.0401","incoming":{"papers":10,"sentences":17,"groups":[{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1006.3548","title":"Deformations of quantum field theories on spacetimes with Killing vector fields","url":"/paper/1006.3548","section":"Geometric setup","sentence":"At the end of that section, we compare our notion of wedges to other definitions which have been made in the literature [ref] , and point out the similarities and differences.","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":4,"sentences":5,"quotes":[{"arxiv_id":"1006.3548","title":"Deformations of quantum field theories on spacetimes with Killing vector fields","url":"/paper/1006.3548","section":"Introduction","sentence":"In fact, different definitions are possible, and wedges on special manifolds have been studied by many authors in the literature [ref] 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which has also been investigated rather extensively from the viewpoint of algebraic quantum field theory [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"0808.2730","title":"On the Advancements of Conformal Transformations and their Associated Symmetries in Geometry and Theoretical Physics","url":"/paper/0808.2730","section":"AdS/CFT correspondence","sentence":"A recent summary of results can be found in the Thesis [ref] .","intent_p":0.86,"contests_p":null}]}],"unlabelled_sentences":11},"outgoing":{"papers":50,"sentences":97,"groups":[{"kind":"extends","label":"Builds on","papers":1,"sentences":3,"quotes":[{"arxiv_id":"hep-th/9905179","title":"Algebraic Holography","url":"/paper/hep-th/9905179","section":"Introduction","sentence":"We adopt as a starting point the theorem demonstrated by Rehren [ref] in the context of Local Quantum Physics (also known as Algebraic Quantum Field Theory) in anti-de Sitter (AdS) spacetimes, called algebraic holography or Rehren duality.","intent_p":0.84,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":14,"sentences":15,"quotes":[{"arxiv_id":"hep-th/0502096","title":"Algebraic holography in asymptotically simple, asymptotically AdS spacetimes","url":"/paper/hep-th/0502096","section":"On the structure of this Thesis","sentence":"This result is original [ref] , and the proof involves an interesting application of the method employed by Penrose [ref] to prove the existence of singularities as result of gravitational collapse, together with a compactness argument, to obtain a geometric maximum principle that guarantees the precise envelope (Theorem [ref], page ch1t9).","intent_p":0.86,"contests_p":null},{"arxiv_id":"math-ph/0112041","title":"The generally covariant locality principle -- A new paradigm for local quantum physics","url":"/paper/math-ph/0112041","section":"Introduction","sentence":"The language employed for the quantum theories relevant for our generalization of Rehren duality follows the functorial formulation of Local Quantum Physics due to Brunetti, Fredenhagen and Verch [ref] , extended afterwards by Sommer [ref] in order to incorporate boundary conditions.","intent_p":0.85,"contests_p":null},{"arxiv_id":"math-ph/9805013","title":"Modular Groups of Quantum Fields in Thermal States","url":"/paper/math-ph/9805013","section":"On the structure of this Thesis","sentence":"Employing the techniques of Borchers and Yngvason [ref] (stated in Theorems [ref], [ref] and [ref], page ch4t1ff.), we shall show that such a condition can be understood as a prescription for the scaling behaviour of observables in a neighborhood of infinity (Proposition [ref], page ch4p1), which can be generalized to asymptotically anti-de Sitter spacetimes.","intent_p":0.94,"contests_p":null},{"arxiv_id":"hep-th/9501063","title":"Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory","url":"/paper/hep-th/9501063","section":"Boundary values as a 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this Thesis","sentence":"The presentation of this Chapter has several improvements with respect to [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"hep-th/9908140","title":"AdS/CFT correspondence for n-point functions","url":"/paper/hep-th/9908140","section":"Boundary values as a dynamical condition","sentence":"The equivalence in item (iv) of Proposition [ref] shows that, indeed, ([ref]) and ([ref]) act effectively as a condition on scaling limits around points in $ℐ$, thus revealing the relation between this set of hypotheses and the formulation of Bertola et al. 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which determine the properties of return to equilibrium, and quasinormal modes of AAdS black holes [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"hep-th/9909056","title":"Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium","url":"/paper/hep-th/9909056","section":"Obstructions to the inversion of Rehren duality","sentence":"An example which motivates such a conjecture is the relation between the poles of retarded two-point functions of the dual quantum theory at the boundary, which determine the properties of return to equilibrium, and quasinormal modes of AAdS black holes [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":6,"sentences":11,"quotes":[{"arxiv_id":"hep-th/9905179","title":"Algebraic Holography","url":"/paper/hep-th/9905179","section":"Locally covariant quantum theories in AdS","sentence":"We conclude this Subsection by outlining, for completeness, the original form of Rehren duality: [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"hep-th/9711200","title":"The Large N Limit of Superconformal Field Theories and Supergravity","url":"/paper/hep-th/9711200","section":"Introduction","sentence":"Within the integrated description of gauge theories and gravity proposed by string theory, two results suggest that this theory may provide a realization of the holographic principle: the microscopic calculation of Bekenstein entropy made by Strominger and Vafa [ref] , and, above all, the work of Maldacena [ref] , which, by means of a(n effective limit of a) string model on the background spacetime $AdS_5×S^5$, where the $AdS_5$ factor is the anti-de Sitter (AdS) spacetime in five dimensions, obtained the field multiplet of a supersymmetric, conformally invariant gauge theory with structural group $SU(N)$ in the $N→∞$ limit, living at the conformal boundary of $AdS_5$ (the $S^5$ factor becomes a global group of internal (R-)symmetries 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unitary implementability of conformal transformations in the GNS Hilbert space of a conformally invariant vacuum by the Tomita-Takesaki modular groups was previously demonstrated by Brunetti, Guido and Longo [ref] .","intent_p":0.81,"contests_p":null}]}],"unlabelled_sentences":60},"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. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/0712.0401"}}