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Large $N$ phase transition in $T \overline{T}$-deformed $2d$ Yang-Mills theory on the sphere
High Energy Physics - Theory · Submitted 12 Oct 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that the Douglas-Kazakov phase transition persists for a range of values of the deformation parameter, and that the critical area is lowered.
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The abstract, sentence by sentence
We study the partition function of a $T \overline{T}$-deformed version of Yang-Mills theory on the two-sphere. We show that the Douglas-Kazakov phase transition persists for a range of values of the deformation parameter, and that the critical area is lowered. The transition is of third order and also induced by instantons, whose contributions we characterize.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the partition function of a $T \overline{T}$-deformed version of Yang-Mills theory on the two-sphere. | contribution 0.96 | 0.88 | 0.04 | asserted 0.68 |
| s1 | We show that the Douglas-Kazakov phase transition persists for a range of values of the deformation parameter, and that the critical area is lowered. | result 1.00 | 0.95 | 0.77 | asserted 1.00 |
| s2 | The transition is of third order and also induced by instantons, whose contributions we characterize. | result 0.99 | 0.89 | 0.22 | asserted 1.00 |
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The paper
Original abstract
We study the partition function of a $T \overline{T}$-deformed version of Yang-Mills theory on the two-sphere. We show that the Douglas-Kazakov phase transition persists for a range of values of the deformation parameter, and that the critical area is lowered. The transition is of third order and also induced by instantons, whose contributions we characterize.
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References
How the literature uses it
24 arXiv papers cite this in 50 sentences
Papers citing it · 24 sentences without a confident label
Builds on it 3 papers
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In this section we shall generalize the 3-rd order phase transition in the deformed large $N$ 2d YM for the sphere [ref] for more generic cases and topologies.
$T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions · Douglas-Kazakov phase transition · 1.00
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A central point of this paper is a generalization of the analysis of [ref] to the large $N$ limit of the $TT$-deformation of $q$-deformed $U(N)$ Yang-Mills theory on the sphere.
$T\overline{T}$-deformation of $q$-Yang-Mills theory · Introduction · 1.00
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Furthermore, it is natural to employ our analysis of the flow equation to extend previous results at large $N$ [ref] .
Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere · Introduction · 0.99
Uses its method or tool 2 papers
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We solve the saddle point equation [ref] perturbatively, as in [ref] and reviewed in Section [ref] above.
$T\overline{T}$-deformation of $q$-Yang-Mills theory · Large $N$ limit of $T T$-deformed $q$-Yang-Mills theory · 0.99
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Now we can proceed according to [ref] and look for the saddle density $ρ_s(A,h)$ perturbatively in $τ$.
$T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions · Phase transition for the disk topology · 0.92
Compares with it 1 paper
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Let us emphasize that $b^+$ exactly coincides with $b_∞$ from [ref] found perturbatively in $τ$.
$T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions · Solution to the equations of motion on the sphere · 0.91
Cites it as background 17 papers
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The partition function and its flow equation were studied in [ref] [ref] [ref] [ref] [ref] [ref] [ref] .
Comments on large central charge $T\bar{T}$ deformed conformal field theory and cutoff AdS holography · Introduction · 1.00
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In the context of the $TT̅$ deformation, Yang–Mills theory was studied in [ref] and its large-$N$ limit was explored in [ref] .
Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere · Introduction · 0.84
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$TT̅$ perturbations of 2d Quantum Field Theories (QFT) [ref] attracted a lot of interest in the past few years mainly due to the fact that they are at the crossroad of several different research lines.
On the $T\bar T$ deformation of the compactified boson and its interpretation in Lattice Gauge Theory · Introduction · 0.99
What it cites · 39 sentences without a confident label
Builds on 2 papers
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We will not be using any of these developments specifically but, rather, will take on the last part of the recent work [ref] , where the $TT$-deformation of two-dimensional Yang–Mills theory [ref] is presented.
Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories · Introduction · 0.83
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We will not be using any of these developments specifically but, rather, will take on the last part of the recent work [ref] , where the $TT$-deformation of two-dimensional Yang–Mills theory [ref] is presented.
Generalised Born-Infeld models, Lax operators and the $\textrm{T} \bar{\textrm{T}}$ perturbation · Introduction · 0.83
Uses the method or tool of 5 papers
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Following the standard procedure for the large $N$ analysis [ref] , we introduce the variables [equation] and, sending $N→∞$, replace $N^-1∑_i=1^N$ with $∫_0^1dx$.
Large $N$ Phase Transition in Continuum QCD$_2$ · Large $N$ limit of the $T T$-deformed theory · 0.98
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We will follow the procedure of [ref] to evaluate the weights $w( ℓ)$ in the $T T$-deformed version of the theory [ref].
Classical Solutions for Two Dimensional QCD on the Sphere · Instanton sectors and Poisson resummation · 0.91
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This implies that, at large $N$, we can perform $N-1$ integrals using the saddle point approximation for the eigenvalue distribution, and eventually treat the integration over $h_1$ separately [ref] .
Instanton Induced Large $N$ Phase Transitions in Two and Four Dimensional QCD · Instantons in the $T T$-deformed theory · 0.81
Compares with 1 paper
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The result is clearly the same as [ref] , up to a rescaling $A↦Ad_k$.
Large $N$ Phase Transition in Continuum QCD$_2$ · Strong coupling phase · 0.98
Cites as background 32 papers
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The large $N$ limit of [ref] was studied in [ref] , showing the presence of a phase transition, known as Douglas–Kazakov (DK) phase transition [ref] .
Classical Solutions for Two Dimensional QCD on the Sphere · Two-dimensional Yang–Mills theory and its $TT$ -deformation · 0.89
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The large $N$ limit of [ref] was studied in [ref] , showing the presence of a phase transition, known as Douglas–Kazakov (DK) phase transition [ref] .
Large $N$ Phase Transition in Continuum QCD$_2$ · Two-dimensional Yang–Mills theory and its $TT$ -deformation · 0.89
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The large $N$ limit of [ref] was studied in [ref] , showing the presence of a phase transition, known as Douglas–Kazakov (DK) phase transition [ref] .
Instanton Induced Large $N$ Phase Transitions in Two and Four Dimensional QCD · Two-dimensional Yang–Mills theory and its $TT$ -deformation · 0.89
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