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

## TL;DR

This paper investigates the long-distance quark-antiquark potential in non-conformal strongly coupled theories using holography, revealing universal correction behaviors related to IR physics and RG flows, with implications for lattice QCD comparisons.

## Contribution

It introduces a general holographic Wilsonian renormalization method to analyze IR corrections to the $qar{q}$ potential in diverse RG flow scenarios, including fixed points and confining theories.

## Key findings

- In theories with IR fixed points, corrections decay as 1/L^4.
- In confining theories, corrections decay exponentially with inter-quark separation.
- The correction behaviors are linked to double-trace deformations and flux tube excitations.

## 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.