Holographic RG flow and reparametrization invariance of Wilson loops

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 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-AdS2 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.

Beyond AdS2/dCFT1: insertions in two Wilson loops

“…This is to be contrasted with the emergent nature of SO(2, 1) in the JT context with its correspondence pseudo-Goldstone mode in the boundary which is related to spontaneously broken reparametrizations. This discussion was addressed, for example, in [60]. More recently, the authors of [27] have clarified that the out-of-time-order correlators in the AdS 2 open string/Wilson loop correspondence display, in the appropriate regime, a Lyapunov growth that saturates the chaos bound.…”