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Intermediate distance correlators in hot Yang-Mills theory
High Energy Physics - Phenomenology · Submitted 19 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We do find unequal results, however the numerical disparity is small.
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The abstract, sentence by sentence
Lattice measurements of spatial correlation functions of the operators FF and FF-dual in thermal SU(3) gauge theory have revealed a clear difference between the two channels at "intermediate" distances, x ~ 1/(pi T). This is at odds with the AdS/CFT limit which predicts the results to coincide. On the other hand, an OPE analysis at short distances (x << 1/(pi T)) as well as effective theory methods at long distances (x >> 1/(pi T)) suggest differences. Here we study the situation at intermediate distances by determining the time-averaged spatial correlators through a 2-loop computation. We do find unequal results, however the numerical disparity is small. Apart from theoretical issues, a future comparison of our results with time-averaged lattice measurements might also be of phenomenological interest in that understanding the convergence of the weak-coupling series at intermediate distances may bear on studies of the thermal broadening of heavy quarkonium resonances.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Lattice measurements of spatial correlation functions of the operators FF and FF-dual in thermal SU(3) gauge theory have revealed a clear difference between the two channels at "intermediate" distances, x ~ 1/(pi T). | background 0.99 | 0.09 | 0.06 | asserted 1.00 |
| s1 | This is at odds with the AdS/CFT limit which predicts the results to coincide. | background 0.90 | 0.05 | 0.05 | asserted 1.00 |
| s2 | On the other hand, an OPE analysis at short distances (x << 1/(pi T)) as well as effective theory methods at long distances (x >> 1/(pi T)) suggest differences. | background 0.95 | 0.09 | 0.04 | hedged possibility 0.87 |
| s3 | Here we study the situation at intermediate distances by determining the time-averaged spatial correlators through a 2-loop computation. | contribution 0.83 | 0.94 | 0.05 | asserted 0.95 |
| s4 | We do find unequal results, however the numerical disparity is small. | result 1.00 | 0.96 | 0.83 | asserted 1.00 |
| s5 | Apart from theoretical issues, a future comparison of our results with time-averaged lattice measurements might also be of phenomenological interest in that understanding the convergence of the weak-coupling series at intermediate distances may bear on studies of the thermal broadening of heavy quarkonium resonances. | future work 0.92 | 0.11 | 0.04 | hedged possibility 0.54 |
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The paper
Original abstract
Lattice measurements of spatial correlation functions of the operators FF and FF-dual in thermal SU(3) gauge theory have revealed a clear difference between the two channels at "intermediate" distances, x ~ 1/(pi T). This is at odds with the AdS/CFT limit which predicts the results to coincide. On the other hand, an OPE analysis at short distances (x << 1/(pi T)) as well as effective theory methods at long distances (x >> 1/(pi T)) suggest differences. Here we study the situation at intermediate distances by determining the time-averaged spatial correlators through a 2-loop computation. We do find unequal results, however the numerical disparity is small. Apart from theoretical issues, a future comparison of our results with time-averaged lattice measurements might also be of phenomenological interest in that understanding the convergence of the weak-coupling series at intermediate distances may bear on studies of the thermal broadening of heavy quarkonium resonances.
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References
How the literature uses it
7 arXiv papers cite this in 13 sentences
Papers citing it · 4 sentences without a confident label
Builds on it 1 paper
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There, the quantity was evaluated to next-to-leading order (NLO) in the limit of vanishing external three-momentum, building on the earlier work of [ref] .
The shear channel spectral function in hot Yang-Mills theory · Introduction · 0.80
Compares with it 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.
Spatial scalar correlator in strongly coupled hot N=4 Yang-Mills theory · The static case $ω=0$ · 1.00
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The result was then Fourier transformed to a spatial Green's function and compared with a computation in next-to-leading order QCD perturbation theory [ref] , see also [ref] .
Frequency and wave number dependence of the shear correlator in strongly coupled hot Yang-Mills theory · Introduction · 0.99
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In Section [ref], we found that the NLO expressions we obtained for the Wilson coefficients of the coordinate space shear correlator, Eqs. ([ref])–([ref]), display considerably improved convergence properties in comparison with those obtained in the bulk channel in Ref. [ref] .
The ultraviolet limit and sum rule for the shear correlator in hot Yang-Mills theory · Discussion and conclusions · 1.00
Cites it as background 2 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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For pure SU($N$) Yang-Mills theory, defined via the Euclidean action (note that we work in Euclidean metric throughout the paper) S_E = ∫_0^β τ∫ d^D-1x⃗ 1/4 F^a_μν F^a_μν ≡ ∫_x 1/4 F^a_μν F^a_μν , with $D≡4-2ϵ$, $β≡1/T$ and F^a_μν ≡ ∂_μA^a_ν- ∂_νA^a_μ+ f^abc A^b_μA^c_ν , a next-to-leading order (NLO) spectral function was first determined in the bulk channel in [ref] , building on the earlier work of [ref] (see also [ref] ).
On the infrared behavior of the shear spectral function in hot Yang-Mills theory · Introduction · 0.84
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