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Spatial scalar correlator in strongly coupled hot N=4 Yang-Mills theory
High Energy Physics - Theory · Submitted 25 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The result is compared with a perturbative computation in finite T SU(N_c) Yang-Mills theory.
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We use AdS/CFT duality to compute in N=4 Yang-Mills theory the finite temperature spatial correlator G(r) of the scalar operator F^2, integrated over imaginary time. The computation is carried out both at zero frequency and integrating the spectral function over frequencies. The result is compared with a perturbative computation in finite T SU(N_c) Yang-Mills theory.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We use AdS/CFT duality to compute in N=4 Yang-Mills theory the finite temperature spatial correlator G(r) of the scalar operator F^2, integrated over imaginary time. | contribution 0.96 | 0.95 | 0.13 | asserted 1.00 |
| s1 | The computation is carried out both at zero frequency and integrating the spectral function over frequencies. | method 0.99 | 0.92 | 0.05 | asserted 0.99 |
| s2 | The result is compared with a perturbative computation in finite T SU(N_c) Yang-Mills theory. | method 0.48 | 0.81 | 0.10 | asserted 0.97 |
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Original abstract
We use AdS/CFT duality to compute in N=4 Yang-Mills theory the finite temperature spatial correlator G(r) of the scalar operator F^2, integrated over imaginary time. The computation is carried out both at zero frequency and integrating the spectral function over frequencies. The result is compared with a perturbative computation in finite T SU(N_c) Yang-Mills theory.
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How the literature uses it
6 arXiv papers cite this in 17 sentences
Papers citing it · 8 sentences without a confident label
Compares with it 3 papers
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It is interesting to contrast these predictions with the corresponding results obtained for the conformal $𝒩=4$ SYM theory in [ref] as well for weakly coupled SU($N$) Yang-Mills theory in [ref] ; a detailed account of these issues will appear soon [ref] .
Bulk and shear spectral functions in weakly and strongly coupled Yang-Mills theory · AdS/CFT duality and IHQCD · 1.00
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Overall, at $10T_c$ the correlators were very close to the conformal situation [ref] , but large effects were observed when $T$ decreased towards $T_c$.
Frequency and wave number dependence of the shear correlator in strongly coupled hot Yang-Mills theory · Conclusions · 0.99
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Comparing to the corresponding result in the conformal $=4$ SYM theory [ref] , whose asymptotic behavior is represented by the dashed blue curve on the left, we see that the effects of conformal invariance breaking are largest near the IHQCD deconfinement temperature $T_c$, while already at $T=10T_c$ the IHQCD result is rather close to the SYM one.
Energy momentum tensor correlators in hot Yang-Mills theory: holography confronts lattice and perturbation theory · Holographic results in the shear channel · 0.99
Cites it as background 4 papers
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Recent lattice studies of energy momentum tensor correlators include at least [ref] , while related perturbative work has been performed in [ref] and holographic calculations in [ref] .
Energy momentum tensor correlators in hot Yang-Mills theory: holography confronts lattice and perturbation theory · Introduction · 0.88
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Moving on to the strong coupling side, we note that spectral functions corresponding to various components of the energy momentum tensor of $𝒩=4$ Super Yang-Mills theory and its variants have been considered using holographic methods in several works, including e.g. [ref] .
Bulk and shear spectral functions in weakly and strongly coupled Yang-Mills theory · AdS/CFT duality and IHQCD · 0.99
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Relevant work on the shear correlator has in addition been carried out in holographic models, cf. e.g. Refs. [ref] .
The ultraviolet limit and sum rule for the shear correlator in hot Yang-Mills theory · Introduction · 0.99
What it cites · 19 sentences without a confident label
Uses the method or tool of 4 papers
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For the Green's function one needs [ref] , expanding near $z=0$, 1z^3ϕ̇_h(z,K)ϕ_h(z,K)= ω^2-k^22z^2-(ω^2-k^2)^216(4logz+3)+4·B(K)A(K)+(z^2). keyeqexp The first two real terms are neglected as contact terms (and they anyway vanish on the light cone) and the result for the Green's function is, including $1/(16πG_5)$ from the gravity action G(K)=^34πG_5B(K)A(K), keyeq where B(K)A(K)=- ϕ_hϕ̇_u-ϕ_uϕ̇_hϕ_hϕ̇_n-ϕ_nϕ̇_h.
Minkowski-space correlators in AdS/CFT correspondence: recipe and applications · Method of numerical solution · 1.00
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Computing $G(ω,)$ and, in particular, the spectral function $ρ(ω,)≡G_R(ω,)$ using the methods of [ref] , the coordinate space Green's function is given by G(τ,)=∫d^3k(2π)^3e^i· ∫_0^∞dωπρ(ω,) cosh(12β-τ)ωsinh12βω. spectrep Integrating this over $τ$ we see that the static correlator is also obtained by evaluating G(r)=12π^2 r∫_0^∞dk k sin(r k) ∫_0^∞dωπ2ρ(ω,k)ω. gkomega We shall show that the same result is obtained via gk and gkomega, though the path via gkomega is much longer.
Thermal spectral functions of strongly coupled N=4 supersymmetric Yang-Mills theory · Introduction · 1.00
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Computing $G(ω,)$ and, in particular, the spectral function $ρ(ω,)≡G_R(ω,)$ using the methods of [ref] , the coordinate space Green's function is given by G(τ,)=∫d^3k(2π)^3e^i· ∫_0^∞dωπρ(ω,) cosh(12β-τ)ωsinh12βω. spectrep Integrating this over $τ$ we see that the static correlator is also obtained by evaluating G(r)=12π^2 r∫_0^∞dk k sin(r k) ∫_0^∞dωπ2ρ(ω,k)ω. gkomega We shall show that the same result is obtained via gk and gkomega, though the path via gkomega is much longer.
On the Absorption by Near-Extremal Black Branes · Introduction · 1.00
Compares with 3 papers
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The finite $T$ part of the full result in res, multiplied by 16, is compared with the NLO computation in [ref] in Fig. [ref]; the leading $1/r^7$ terms are the same.
Intermediate distance correlators in hot Yang-Mills theory · The static case $ω=0$ · 1.00
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Motivated by needs of lattice work [ref] , we have in this article computed the $r$ dependence of the $τ$ integrated finite temperature correlator $⟨F^2(τ,)F^2(0,0)⟩$ and compared it with the same in SU($N_c$) Yang-Mills theory [ref] .
Energy-momentum tensor correlators and spectral functions · Conclusions · 0.97
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Comparing with the next-to-leading order computation in SU($N_c$) Yang-Mills theory [ref] one notes that the leading UV terms[The leading diagram of the $F^2$ correlator is reduced to scalar master integrals in Eq. (3.1) of [ref] .
Ultraviolet asymptotics of scalar and pseudoscalar correlators in hot Yang-Mills theory · The static case $ω=0$ · 1.00
Cites as background 1 paper
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An AdS/CFT computation of $G(τ,r)$ has been presented in [ref] .
Spatial correlators in strongly coupled plasmas · Introduction · 0.86
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