Flux tube profile from Holography: finite size and strong coupling corrections

TL;DR

This work employs holography to compute the classical flux tube profile between a static quark–antiquark pair in a confining $2+1$-D large-$N$ gauge theory, incorporating finite inter-quark distance and the first subleading strong-coupling corrections. The authors establish a holographic dictionary linking the on-shell dilaton field to the flux-tube profile, solve the dilaton equation of motion for the LO and NLO corrections sourced by a classical fundamental string, and derive a general, non-analytic expression for the profile across the boundary. A key result is the identification of the intrinsic width with the inverse mass of the lightest scalar glueball, maintaining this relation at NLO in the strong coupling expansion, and they provide a semi-analytical method to compute glueball mass corrections. They also discuss the large-L broadening, a qualitative bridge between Abrikosov-vortex and EST descriptions, and outline how quantum fluctuations can be incorporated via world-sheet dynamics, including a convolution structure that reproduces known logarithmic broadening behavior. Overall, the paper delivers a comprehensive holographic framework linking flux-tube structure, intrinsic width, and glueball spectra in a confining gauge theory.

Abstract

We use the holographic correspondence as a tool to study the classical flux tube profile connecting a static quark-antiquark pair in a $2+1$-dimensional strongly-coupled large $N$ QCD-like theory. The final result extends already known findings in the literature in several ways. First, it is an analytical function of both the space-like boundary coordinates; in other words, we keep track of what happens both along and transversely to the inter-quark axis. Then, we take into account the finiteness of the inter-quark distance and the first correction in the strong coupling expansion. To the same order, we also confirm the relation between the mass of the lightest glueball in the spectrum and the intrinsic width of the flux tube profile. We conclude by trying to gain some insights about the quantum fluctuations. Intriguingly, our proposal is in agreement with widespread expectations in the literature. En passant, we also derive a semi-analytical formula that gives the first correction to the scalar glueball masses in the strong coupling expansion.