Effective long distance $$ q\overline{q} $$ potential in holographic RG flows

Abstract

We study the qq 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 ∼ 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 ∼ e −M L , 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.

Holographic RG flow and reparametrization invariance of Wilson Loops

“…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 [4,5]. It should be noted that a Schwarzian action for transverse fluctuations can also appear when the string is embedded in AdS 3 [24,25], but it is related to diffeomorphisms in the target space, rather than to worldsheet transformations.…”

“…For a 1/2 BPS loop, or at lower order in perturbation theory, the defect action of a straight or circular Wilson loop is reparametrization invariant [27] and this reduces the calculation of the expectation value to a random matrix integral. The SYK model could be seen similarly as a 0+1 defect theory 4 , where reparametrization invariance emerges at low energies. Contrary to the Wilson loop, in this case it is not a true symmetry, and there is a Schwarzian effective action for reparametrizations.…”

“…Then, by fitting the coefficients of the cutoff action, one may be able to capture the right UV physics in the holographic dual, while remaining in the region where gravity is weakly coupled. For Wilson loops, which is our topic of interest here, the cutoff action has been studied in [4,5], following the general approach of holographic Wilsonian renormalization [6,7]. Wilson loops provide a complete set of gauge invariant operators that could in principle be used to compute any observable in Yang-Mills theory, and determine directly some important phenomenological quantities like the quark-antiquark potential.…”

Holographic Wilsonian renormalization of a heavy quark moving through a strongly coupled plasma

“…of holographic "Wilsonian" renormalization [33,34] to a moving string. Our analysis is an extension of [35], 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

“…the method of holographic "Wilsonian" renormalization [33,34] to a moving string. Our analysis is an extension of [35], where we applied this method to static strings in order to extract the quark-antiquark potential.…”