{"arxiv_id":"2204.13636","incoming":{"papers":3,"sentences":4,"groups":[{"kind":"background","label":"Cites it as background","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2503.09997","title":"$T\\overline{T}$ Deformation: Introduction and Some Recent Advances","url":"/paper/2503.09997","section":"Introduction","sentence":"As this area of research grows, we expect this review will help identify new connections and directions in the study of quantum gravity [ref] , holography [ref] , and string theory [ref] .","intent_p":0.8,"contests_p":null}]}],"unlabelled_sentences":3},"outgoing":{"papers":65,"sentences":135,"groups":[{"kind":"extends","label":"Builds on","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2106.01375","title":"Nonperturbative effects and resurgence in JT gravity at finite cutoff","url":"/paper/2106.01375","section":"Gravity side","sentence":"Based on JT results [ref] Z_JT,D (u,t) =u/√(t)e^-u/t/u^2+4π^2 tI_2(1/t√(u^2+4π^2 t)) Z_JT,D (u,t) = u/√(t)e^-u/t/√(u^2-b^2t)I_1(1/t√(u^2-b^2 t)), u=2β, where $I_1,I_2$ are modified Bessel functions.","intent_p":0.8,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":5,"sentences":7,"quotes":[{"arxiv_id":"2004.07242","title":"JT gravity at finite cutoff","url":"/paper/2004.07242","section":"Introduction","sentence":"The deformed disk and trumpet partition function can be worked out by applying the techniques developed in [ref] as well as the method in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2106.01375","title":"Nonperturbative effects and resurgence in JT gravity at finite cutoff","url":"/paper/2106.01375","section":"Introduction","sentence":"The deformed disk and trumpet partition function can be worked out by applying the techniques developed in [ref] as well as the method in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1510.04430","title":"Random matrices","url":"/paper/1510.04430","section":"$R^Q_0,2$","sentence":"[$W̅_2(x_1,x_2)$ in [ref] is $R^Q_0,2(x_1,x_2)$ here.] Transforming to uniformized coordinate $z_i$ by the map ((3.3.15) of that paper $a=-b$) x=a/2(z+1/z), where $z$ is double cover of $x$ (similar to the map $x=-z^2$ appeared in the JT case).","intent_p":0.88,"contests_p":null},{"arxiv_id":"hep-th/0407261","title":"All genus correlation functions for the hermitian 1-matrix model","url":"/paper/hep-th/0407261","section":"Type 0A","sentence":"This is follows from $R^SJT-_0,2(E_1,E_2,t) =4R^ JT_0,2(E_1,E_2,t)$ (see ([ref])).] To compute $R^-_g,n(E_1,...,E_n,t)$ in matrix model, one can employ a power tool called topological recursion relation [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"2004.01171","title":"Notes on Matrix Models","url":"/paper/2004.01171","section":"Equation ([ref])","sentence":"It follows that in the orthogonal polynomial method (for example, see [ref] ), the orthogonal polynomials $P_n(x)$ have definite parity, i.e., being even or odd of $x$.","intent_p":0.86,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2004.07242","title":"JT gravity at finite cutoff","url":"/paper/2004.07242","section":"Introduction","sentence":"The result was consistent with [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2106.01375","title":"Nonperturbative effects and resurgence in JT gravity at finite cutoff","url":"/paper/2106.01375","section":"Gravity side","sentence":"Notice that $ρ_SJT,D(E,t)$ is negative in the range $(2/t,4/t)$, which is similar with JT case [ref] .","intent_p":0.95,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2004.07242","title":"JT gravity at finite cutoff","url":"/paper/2004.07242","section":"Gravity side","sentence":"Moreover, when both branches are taken into consideration, the $TT̅$ flow equation will be satisfied and the complex spectrum problem mentioned above will disappear [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":40,"sentences":52,"quotes":[{"arxiv_id":"1903.11115","title":"JT gravity as a matrix integral","url":"/paper/1903.11115","section":"Basic facts","sentence":"We mainly follow the discussions in [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2111.09330","title":"Phase transitions for deformations of JT supergravity and matrix models","url":"/paper/2111.09330","section":"Basic facts","sentence":"We mainly follow the discussions in [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1907.03363","title":"JT Gravity and the Ensembles of Random Matrix Theory","url":"/paper/1907.03363","section":"Basic facts","sentence":"We mainly follow the discussions in [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2012.11714","title":"$T\\bar{T}$ deformation of random matrices","url":"/paper/2012.11714","section":"Introduction","sentence":"In the present work, we are interested in the JT and SJT/ matrix model duality with $TT̅$ deformation [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"2202.03454","title":"$T\\overline{T}$-deformed free energy of the Airy model","url":"/paper/2202.03454","section":"Introduction","sentence":"In the present work, we are interested in the JT and SJT/ matrix model duality with $TT̅$ deformation [ref] .","intent_p":0.87,"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. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2204.13636"}}