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Effective long distance $q\bar{q} $ potential in holographic RG flows
High Energy Physics - Theory · Submitted 12 Feb 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In both cases, we find corrections with a universal dependence on the inter-quark separation.
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The abstract, sentence by sentence
We study the $q\bar{q}$ potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. We focus on the properties of this potential at an inter-quark separation $L$ large compared to the characteristic scale of the field theory. These are determined by the leading order IR physics plus a series of corrections, sensitive to the properties of the RG-flow. To determine those corrections, we propose a general method applying holographic Wilsonian renormalization to a dual string. We apply this method to examine in detail two sets of examples, $3+1$-dimensional theories with an RG flow ending in an IR fixed point; and theories that are confining in the IR, in particular, the Witten QCD and Klebanov-Strassler models. In both cases, we find corrections with a universal dependence on the inter-quark separation. When there is an IR fixed point, that correction decays as a power $\sim 1/L^4$. We explain that dependence in terms of a double-trace deformation in a one-dimensional defect theory. For a confining theory, the decay is exponential $\sim e^{-ML}$, with $M$ a scale of the order of the glueball mass. We interpret this correction using an effective flux tube description as produced by a background internal mode excitation induced by sources localized at the endpoints of the flux tube. We discuss how these results could be confronted with lattice QCD data to test whether the description of confinement via the gauge/gravity is qualitatively correct.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the $q\bar{q}$ potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. | contribution 0.91 | 0.87 | 0.04 | asserted 0.91 |
| s1 | We focus on the properties of this potential at an inter-quark separation $L$ large compared to the characteristic scale of the field theory. | contribution 0.74 | 0.45 | 0.03 | asserted 0.83 |
| s2 | These are determined by the leading order IR physics plus a series of corrections, sensitive to the properties of the RG-flow. | result 0.64 | 0.35 | 0.13 | asserted 1.00 |
| s3 | To determine those corrections, we propose a general method applying holographic Wilsonian renormalization to a dual string. | method 0.91 | 0.73 | 0.05 | asserted 0.88 |
| s4 | We apply this method to examine in detail two sets of examples, $3+1$-dimensional theories with an RG flow ending in an IR fixed point; and theories that are confining in the IR, in particular, the Witten QCD and Klebanov-Strassler models. | contribution 0.84 | 0.88 | 0.06 | asserted 0.97 |
| s5 | In both cases, we find corrections with a universal dependence on the inter-quark separation. | result 1.00 | 0.96 | 0.33 | asserted 1.00 |
| s6 | When there is an IR fixed point, that correction decays as a power $\sim 1/L^4$. | result 1.00 | 0.93 | 0.20 | asserted 1.00 |
| s7 | We explain that dependence in terms of a double-trace deformation in a one-dimensional defect theory. | interpretation 1.00 | 0.82 | 0.07 | asserted 1.00 |
| s8 | For a confining theory, the decay is exponential $\sim e^{-ML}$, with $M$ a scale of the order of the glueball mass. | result 1.00 | 0.92 | 0.17 | asserted 1.00 |
| s9 | We interpret this correction using an effective flux tube description as produced by a background internal mode excitation induced by sources localized at the endpoints of the flux tube. | interpretation 1.00 | 0.80 | 0.10 | asserted 0.89 |
| s10 | We discuss how these results could be confronted with lattice QCD data to test whether the description of confinement via the gauge/gravity is qualitatively correct. | future work 0.99 | 0.21 | 0.05 | hedged possibility 0.99 |
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The paper
Original abstract
We study the $q\bar{q}$ potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. We focus on the properties of this potential at an inter-quark separation $L$ large compared to the characteristic scale of the field theory. These are determined by the leading order IR physics plus a series of corrections, sensitive to the properties of the RG-flow. To determine those corrections, we propose a general method applying holographic Wilsonian renormalization to a dual string. We apply this method to examine in detail two sets of examples, $3+1$-dimensional theories with an RG flow ending in an IR fixed point; and theories that are confining in the IR, in particular, the Witten QCD and Klebanov-Strassler models. In both cases, we find corrections with a universal dependence on the inter-quark separation. When there is an IR fixed point, that correction decays as a power $\sim 1/L^4$. We explain that dependence in terms of a double-trace deformation in a one-dimensional defect theory. For a confining theory, the decay is exponential $\sim e^{-ML}$, with $M$ a scale of the order of the glueball mass. We interpret this correction using an effective flux tube description as produced by a background internal mode excitation induced by sources localized at the endpoints of the flux tube. We discuss how these results could be confronted with lattice QCD data to test whether the description of confinement via the gauge/gravity is qualitatively correct.
Human review
How the literature uses it
4 arXiv papers cite this in 6 sentences
Papers citing it · 3 sentences without a confident label
Builds on it 2 papers
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Our analysis is an extension of [ref] , where we applied this method to static strings in order to extract the quark-antiquark potential.
Holographic Wilsonian renormalization of a heavy quark moving through a strongly coupled plasma · Introduction · 1.00
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Another interesting extension of this work would be to include in the analysis non-trivial profiles of the string in the transverse directions, generalizing the results of [ref] .
Holographic RG flow and reparametrization invariance of Wilson Loops · Discussion · 0.83
Cites it as background 1 paper
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Wilson loops in various holographic RG flows were studied in [ref] - [ref] .
Wilson loops in exact holographic RG flows at zero and finite temperature · Introduction · 0.94
What it cites · 50 sentences without a confident label
Uses the method or tool of 9 papers
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We will follow the procedure introduced in [ref] , where the evolution of the coefficients in the boundary action is derived from a Hamilton-Jacobi type of equation.
Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm · RG flow evolution of the boundary action · 1.00
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In order to simplify the discussion we will use the `fake' supergravity formalism [ref] ,[The formalism can be derived from a Hamilton-Jacobi formulation of the radial evolution of the solutions, which has also been interpreted in terms of the RG flow in the holographic dual, see e.g. [ref] and [ref] for an earlier work in the context of cosmology.] such that the equations of motion for the metric and the scalar reduce to a system of first order equations.
Exotic RG Flows from Holography · Theory with an IR fixed point · 0.95
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In order to simplify the discussion we will use the `fake' supergravity formalism [ref] ,[The formalism can be derived from a Hamilton-Jacobi formulation of the radial evolution of the solutions, which has also been interpreted in terms of the RG flow in the holographic dual, see e.g. [ref] and [ref] for an earlier work in the context of cosmology.] such that the equations of motion for the metric and the scalar reduce to a system of first order equations.
On multi-field flows in gravity and holography · Theory with an IR fixed point · 0.95
Compares with 3 papers
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Note that while the exponential correction looks somewhat similar to the contributions from a rigidity term [ref] (see [ref] for recent lattice calculations in $2+1$ dimensions), those would be suppressed at strong 't Hooft coupling, and the coefficient of the exponential would decrease at long separations as $∼1/L^1/2$, unlike the contribution we have identified.
A different kind of string · Discussion · 0.97
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Note that while the exponential correction looks somewhat similar to the contributions from a rigidity term [ref] (see [ref] for recent lattice calculations in $2+1$ dimensions), those would be suppressed at strong 't Hooft coupling, and the coefficient of the exponential would decrease at long separations as $∼1/L^1/2$, unlike the contribution we have identified.
Spectrum of the open QCD flux tube and its effective string description I: 3d static potential in SU(N=2,3) · Discussion · 0.97
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Note that while the exponential correction looks somewhat similar to the contributions from a rigidity term [ref] (see [ref] for recent lattice calculations in $2+1$ dimensions), those would be suppressed at strong 't Hooft coupling, and the coefficient of the exponential would decrease at long separations as $∼1/L^1/2$, unlike the contribution we have identified.
Spectrum of the open QCD flux tube and its effective string description · Discussion · 0.97
Cites as background 35 papers
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Although there are several different realizations of confining theories in holography, [ For the general conditions on the metric under which the Wilson loop will show area law in a given holographic model see [ref] .] in this work we will focus on two model examples.
$Q \bar{Q}$ Potential from Strings in Curved Spacetime - Classical Results · Confining theories · 0.91
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The study of Wilson loops in holographic duals was initiated in [ref] .
Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity · Wilson loops in holography · 1.00
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The study of Wilson loops in holographic duals was initiated in [ref] .
Wilson loops in large N field theories · Wilson loops in holography · 1.00
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