{"arxiv_id":"2409.00746","incoming":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"outgoing":{"papers":14,"sentences":37,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1709.02213","title":"On integrability of 2-dimensional $\\sigma$-models of Poisson-Lie type","url":"/paper/1709.02213","section":"Introduction","sentence":"This means that we formulate each of the three models as the $$-models on appropriate Drinfeld doubles and then we try to find out whether a sufficient condition of $$-model integrability [ref] can be applied.","intent_p":0.97,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":3,"sentences":11,"quotes":[{"arxiv_id":"2311.09301","title":"An elliptic integrable deformation of the Principal Chiral Model","url":"/paper/2311.09301","section":"Introduction","sentence":"In the case of the first two families [ref] and [ref], a suitable ansatz for the $$-model Lax matrix completely reproduces the results of [ref] which were obtained by non-$$-models methods.","intent_p":0.97,"contests_p":null},{"arxiv_id":"2406.18523","title":"Integrability and renormalizability for the fully anisotropic ${\\rm SU}(2)$ principal chiral field and its deformations","url":"/paper/2406.18523","section":"Introduction","sentence":"In the case of the first two families [ref] and [ref], a suitable ansatz for the $$-model Lax matrix completely reproduces the results of [ref] which were obtained by non-$$-models methods.","intent_p":0.97,"contests_p":null},{"arxiv_id":"1405.7803","title":"Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model","url":"/paper/1405.7803","section":"RG flow of the non-deformed model","sentence":"We choose the basis of $$ as $T_A$, $A=1,…, 6$ [equation] Using the notation of Section 2.3, we then find [equation] [equation] [equation] Inserting all this in [ref], we obtain precisely the RG flows of the couplings $D_1,D_2,D_3$ which were obtained in [ref] without using the $$-models formalism: dD_1/dμ=-4K^2K^3/D_2D_3, dD_2/dμ=-4K^3K^1/D_3D_1, dD_3/dμ=-4K^1K^2/D_1D_2.","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":25},"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/2409.00746"}}