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Holographic RG flow and reparametrization invariance of Wilson Loops
High Energy Physics - Theory · Submitted 22 Apr 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We make explicit the map between Wilson loop reparametrizations and conformal transformation of the string worldsheet and show that a cutoff anchored to the worldsheet breaks conformal invariance and induces an effective defect action for reparametrizations at the cutoff scale, in a way similar to nearly-$AdS_2$ gravity or SYK models.
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The abstract, sentence by sentence
We study the fate of reparametrization invariance of Wilson loops, also known as 'zig-zag' symmetry, under the RG flow using some simple cases as guidance. We restrict our analysis to large-$N$, strongly coupled CFTs and use the holographic dual description of a Wilson loop as a fundamental string embedded in asymptotically AdS spaces, at zero and nonzero temperature. We then introduce a cutoff in the holographic radial direction and integrate out the the section of the string closer to the AdS boundary in the spirit of holographic Wilsonian renormalization. We make explicit the map between Wilson loop reparametrizations and conformal transformation of the string worldsheet and show that a cutoff anchored to the worldsheet breaks conformal invariance and induces an effective defect action for reparametrizations at the cutoff scale, in a way similar to nearly-$AdS_2$ gravity or SYK models. On the other hand, a cutoff in the target space breaks worldsheet diffeomorphisms and Weyl transformations but keeps conformal transformations unbroken and does not generate a non-trivial action for reparametrizations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the fate of reparametrization invariance of Wilson loops, also known as 'zig-zag' symmetry, under the RG flow using some simple cases as guidance. | contribution 0.96 | 0.85 | 0.07 | unclear 0.79 |
| s1 | We restrict our analysis to large-$N$, strongly coupled CFTs and use the holographic dual description of a Wilson loop as a fundamental string embedded in asymptotically AdS spaces, at zero and nonzero temperature. | method 0.80 | 0.85 | 0.03 | asserted 0.92 |
| s2 | We then introduce a cutoff in the holographic radial direction and integrate out the the section of the string closer to the AdS boundary in the spirit of holographic Wilsonian renormalization. | method 0.99 | 0.92 | 0.04 | asserted 0.94 |
| s3 | We make explicit the map between Wilson loop reparametrizations and conformal transformation of the string worldsheet and show that a cutoff anchored to the worldsheet breaks conformal invariance and induces an effective defect action for reparametrizations at the cutoff scale, in a way similar to nearly-$AdS_2$ gravity or SYK models. | result 0.95 | 0.92 | 0.48 | asserted 1.00 |
| s4 | On the other hand, a cutoff in the target space breaks worldsheet diffeomorphisms and Weyl transformations but keeps conformal transformations unbroken and does not generate a non-trivial action for reparametrizations. | result 1.00 | 0.87 | 0.23 | asserted 1.00 |
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The paper
Original abstract
We study the fate of reparametrization invariance of Wilson loops, also known as 'zig-zag' symmetry, under the RG flow using some simple cases as guidance. We restrict our analysis to large-$N$, strongly coupled CFTs and use the holographic dual description of a Wilson loop as a fundamental string embedded in asymptotically AdS spaces, at zero and nonzero temperature. We then introduce a cutoff in the holographic radial direction and integrate out the the section of the string closer to the AdS boundary in the spirit of holographic Wilsonian renormalization. We make explicit the map between Wilson loop reparametrizations and conformal transformation of the string worldsheet and show that a cutoff anchored to the worldsheet breaks conformal invariance and induces an effective defect action for reparametrizations at the cutoff scale, in a way similar to nearly-$AdS_2$ gravity or SYK models. On the other hand, a cutoff in the target space breaks worldsheet diffeomorphisms and Weyl transformations but keeps conformal transformations unbroken and does not generate a non-trivial action for reparametrizations.
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How the literature uses it
2 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 1 paper
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Some works [ref] have identified Schwarzian effective actions that appear in the dynamics of strings in AdS and have suggested that they may explain the maximal chaos of the AdS string that was noted in [ref] .
Chaos and the reparametrization mode on the AdS$_2$ string · Comparing the string reparametrization mode and the Schwarzian · 0.82
What it cites · 23 sentences without a confident label
Builds on 2 papers
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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] .
Effective long distance $q\bar{q} $ potential in holographic RG flows · Discussion · 0.83
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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 Wilsonian renormalization of a heavy quark moving through a strongly coupled plasma · Discussion · 0.83
Cites as support 1 paper
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This is true at strong coupling even for 1/2 BPS Wilson loops as noted in [ref] , even though the coupling to the scalar fields in principle breaks the zig-zag symmetry.
Wilson Loops and Minimal Surfaces · Introduction · 0.98
Cites as background 4 papers
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For a CFT like $N=4$ super Yang-Mills, the holographic dual of the Wilson loop is a fundamental string anchored at the asymptotic $AdS$ boundary of the gravity dual geometry [ref] .
Wilson loops in large N field theories · Introduction · 0.80
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Gauge/gravity duality has been extensively used as a phenomenological tool to describe strongly coupled systems in particle physics and condensed matter (see e.g. [ref] ).
QCD and strongly coupled gauge theories: challenges and perspectives · Introduction · 1.00
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Gauge/gravity duality has been extensively used as a phenomenological tool to describe strongly coupled systems in particle physics and condensed matter (see e.g. [ref] ).
TASI Lectures on Applications of Gauge/Gravity Duality · Introduction · 1.00
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