论文标题
Wilson Loop的全息RG流量和再现不变性
Holographic RG flow and reparametrization invariance of Wilson Loops
论文作者
论文摘要
我们使用一些简单的情况作为指导，研究了Wilson Loops（也称为“ Zig-Zag”对称性）的Wilson Loops（也称为“ Zig-Zag”对称性）的命运。我们将分析限制为大$ n $，强烈耦合的CFT，并将Wilson环的全息二重描述用作嵌入在零温度和非零温度下的渐近广告空间中的基本弦。然后，我们在全息径向方向上引入了一个截止，并以全息化Wilsonian重新归一化的精神整合了绳子的截面。我们明确说明Wilson Loop Reparamatization和String Worldsheet之间的地图之间的地图，并表明固定在世界表格上的截止值破坏了保形的不变性，并在与几乎 - $ ADS_2 $ GRAVITY或SYK模型类似的方式上促进了在截止量表上进行修复的有效缺陷动作。另一方面，目标空间中的截止时间破坏了世界表格的差异和WEYL变换，但使保形转换不完整，并且不会为重新分析产生非平凡的动作。
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.
