Dynamics of Flux Tubes in Large N Gauge Theories

TL;DR

The paper investigates the dynamics and excitations of a flux tube between a static quark and antiquark in the large $N$ limit, contrasting weak-coupling ladder analyses with strong-coupling AdS/CFT predictions for ${\cal N}=4$ SYM. It demonstrates a coupling-dependent transition from a gapped spectrum at weak coupling to a rich stringy spectrum at strong coupling, including an infinite set of near-threshold states that match ladder-model density under certain conditions. It also shows that long-distance, local-operator correlators exhibit consistent scaling between weak and strong coupling, while adjoint Wilson lines display a distinct fall-to-center behavior at strong coupling. The results provide a coherent, string-theoretic picture of flux-tube excitations and offer qualitative guidance for QCD-like flux tubes and potential gluonic excitations in heavy-quarkonia. Overall, the work highlights how AdS/CFT encodes the flux-tube spectrum and connects it to planar diagram dynamics across coupling regimes.

Abstract

The gluonic field created by a static quark anti-quark pair is described via the AdS/CFT correspondence by a string connecting the pair which is located on the boundary of AdS. Thus the gluonic field in a strongly coupled large N CFT has a stringy spectrum of excitations. We trace the stability of these excitations to a combination of large N suppressions and energy conservation. Comparison of the physics of the N=infinity flux tube in the {\cal N}=4 SYM theory at weak and strong coupling shows that the excitations are present only above a certain critical coupling. The density of states of a highly excited string with a fold reaching towards the horizon of AdS is in exact agreement at strong coupling with that of the near-threshold states found in a ladder diagram model of the weak-strong coupling transition. We also study large distance correlations of local operators with a Wilson loop, and show that the fall off at weak coupling and N=infinity (i.e. strictly planar diagrams) matches the strong coupling predictions given by the AdS/CFT correspondence, rather than those of a weakly coupled U(1) gauge theory.

Figures (4)

• Figure 1: Some Coulomb gauge Feynman diagrams contributing to the Wilson loop. The wavy lines represent transverse gluons and the dashed lines instantaneous Coulomb exchange. The Coulomb exchange diagrams (a) sum up to the ground state pole in $R(E)$. The planar diagram (b) gives a contribution to the continuum cut $E\geq0$. The gap destroying nonplanar diagram (c) is suppressed at $N=\infty$.
• Figure 2: In (a) we show the string going between two points in the boundary which gives the dual description of the flux tube going between the quark and the anti-quark. In (b) we stretch the string up to a large $z_M \gg z_m$. In (c) we replace the stretched string in (b) by a folded string sitting at a single spatial point on the boundary.
• Figure 3: In (a) we show a configuration of a string stretched in the $z$ direction with pieces along the string carrying momentum along the $z$ direction. To facilitate visualization we have separated the strings in a transverse dimension, but we should think of all of the pieces as lying on top of each other as in (b).
• Figure 4: In (a) we see the diagrams contributing to the naive answer. It contains diagrams where the propagator endpoints are separated by a distance of the order of $\Delta t \sim 1/x$. In (b) we take into account the diagrams contributing to Coulomb energy between the quark and antiquark. Planarity plus energetic considerations effectively restrict the endpoints of the propagators to be within $\Delta t \sim 1/E_0$. In (c) we replace the square in the center of (b) by the insertion of a series of operators which is also integrated along $t$, the direction of the original contour.