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Note on $T\bar{T}$ deformed matrix models and JT supergravity duals
High Energy Physics - Theory · Submitted 28 Apr 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We check that the partition functions finite cut-off 0A and 0B SJT on generic 2D surfaces match the associated correlation functions in $T\bar{T}$ deformed matrix models respectively.
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In this work we calculate the partition functions of $\mathcal{N}=1$ type 0A and 0B JT supergravity (SJT) on 2D surfaces of arbitrary genus with multiple finite cut-off boundaries, based on the $T\bar{T}$ deformed super-Schwarzian theories. In terms of SJT/matrix model duality, we compute the corresponding correlation functions in the $T\bar{T}$ deformed matrix model side by using topological recursion relations as well as the transformation properties of topological recursion relations under $T\bar{T}$ deformation. We check that the partition functions finite cut-off 0A and 0B SJT on generic 2D surfaces match the associated correlation functions in $T\bar{T}$ deformed matrix models respectively.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this work we calculate the partition functions of $\mathcal{N}=1$ type 0A and 0B JT supergravity (SJT) on 2D surfaces of arbitrary genus with multiple finite cut-off boundaries, based on the $T\bar{T}$ deformed super-Schwarzian theories. | contribution 1.00 | 0.96 | 0.16 | asserted 1.00 |
| s1 | In terms of SJT/matrix model duality, we compute the corresponding correlation functions in the $T\bar{T}$ deformed matrix model side by using topological recursion relations as well as the transformation properties of topological recursion relations under $T\bar{T}$ deformation. | method 0.86 | 0.95 | 0.09 | asserted 1.00 |
| s2 | We check that the partition functions finite cut-off 0A and 0B SJT on generic 2D surfaces match the associated correlation functions in $T\bar{T}$ deformed matrix models respectively. | result 0.99 | 0.95 | 0.77 | asserted 0.99 |
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The paper
Original abstract
In this work we calculate the partition functions of $\mathcal{N}=1$ type 0A and 0B JT supergravity (SJT) on 2D surfaces of arbitrary genus with multiple finite cut-off boundaries, based on the $T\bar{T}$ deformed super-Schwarzian theories. In terms of SJT/matrix model duality, we compute the corresponding correlation functions in the $T\bar{T}$ deformed matrix model side by using topological recursion relations as well as the transformation properties of topological recursion relations under $T\bar{T}$ deformation. We check that the partition functions finite cut-off 0A and 0B SJT on generic 2D surfaces match the associated correlation functions in $T\bar{T}$ deformed matrix models respectively.
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How the literature uses it
3 arXiv papers cite this in 4 sentences
Papers citing it · 3 sentences without a confident label
Cites it as background 1 paper
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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] .
$T\overline{T}$ Deformation: Introduction and Some Recent Advances · Introduction · 0.80
What it cites · 72 sentences without a confident label
Builds on 1 paper
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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.
Nonperturbative effects and resurgence in JT gravity at finite cutoff · Gravity side · 0.80
Uses the method or tool of 5 papers
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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] .
JT gravity at finite cutoff · Introduction · 1.00
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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] .
Nonperturbative effects and resurgence in JT gravity at finite cutoff · Introduction · 1.00
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[$W̅_2(x_1,x_2)$ 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).
Random matrices · $R^Q_0,2$ · 0.88
Compares with 2 papers
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The result was consistent with [ref] .
JT gravity at finite cutoff · Introduction · 0.99
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Notice that $ρ_SJT,D(E,t)$ is negative in the range $(2/t,4/t)$, which is similar with JT case [ref] .
Nonperturbative effects and resurgence in JT gravity at finite cutoff · Gravity side · 0.95
Cites as support 1 paper
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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] .
JT gravity at finite cutoff · Gravity side · 0.99
Cites as background 40 papers
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We mainly follow the discussions in [ref] .
JT gravity as a matrix integral · Basic facts · 0.99
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We mainly follow the discussions in [ref] .
Phase transitions for deformations of JT supergravity and matrix models · Basic facts · 0.99
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We mainly follow the discussions in [ref] .
JT Gravity and the Ensembles of Random Matrix Theory · Basic facts · 0.99
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