Yang-Mills Flux Tube in AdS II: Effective String Theory

Abstract

We continue the study of flux tubes in confining gauge theories placed in a rigid AdS background, focusing on the three-dimensional case. Our analysis is performed in the large-radius regime, where effective string theory provides a good approximation of the dynamics. Using a combination of techniques, primarily the analytic transcendentality ansatz bootstrap, we compute observables up to two-loop order in the expansion in powers of the string length over the AdS radius, which constitutes the main result of this work. Finally, we employ Padé resummations to explore the possible compatibility of our results with a smooth interpolation of observables between large-radius AdS and small-radius AdS, in which gauge theory is weakly coupled.

Figures (9)

• Figure 1: Effective string
• Figure 2: For each operator on the flux tube in AdS, we plot its dimensions, $(\Delta^{\rm EST},\Delta^{\rm WL})$, in the free limits of both the EST and Wilson line descriptions. These pairs as determined within each global symmetry sector using the no-crossing rule. The map between $\Delta^{\rm EST}$ and $\Delta^{\rm WL}$ is remarkably smooth and uniform across the four symmetry sectors for all dimensions.
• Figure 3: (Supersymmetric Wilson line in $\mathcal{N}=4$ SYM). Various Padé approximants for the norm of the displacement.
• Figure 4: (Supersymmetric Wilson line in $\mathcal{N}=4$ SYM). Various Padé approximants for $\Delta_{\Psi_2}$ (left column) and the relative error compared with exact results from QSC (right column). First row:$[2/1]$ and $[1/2]$ Padé approximants with $O(\sigma^2)$ and $O((1-\sigma)^0)$ perturbative input. Second row:$[2/2]$, $[1/3]$, $[3/1]$ Padé approximants with $O(\sigma^3)$ and $O((1-\sigma)^0)$ perturbative input, which is analogous to what we currently have for the Yang-Mills flux tube. Third row:$[2/3]$ and $[3/2]$ Padé approximants with $O(\sigma^3)$ and $O((1-\sigma)^1)$ perturbative. Fourth row:$[4/2]$, $[3/3]$, $[2/4]$ Padé approximants with $O(\sigma^3)$ and $O((1-\sigma)^2)$ perturbative input.
• Figure 5: (Supersymmetric Wilson line in $\mathcal{N}=4$ SYM). Various Padé approximants for $\Delta_{\Psi_3}$ (left column) and the relative error compared with exact results from QSC (right column). First row:$[2/1]$ and $[1/2]$ Padé approximants with $O(\sigma^2)$ and $O((1-\sigma)^0)$ perturbative input. Second row:$[2/2]$, $[1/3]$, $[3/1]$ Padé approximants with $O(\sigma^3)$ and $O((1-\sigma)^0)$ perturbative input, which is analogous to what we currently have for the Yang-Mills flux tube. Third row:$[2/3]$ and $[3/2]$ Padé approximants with $O(\sigma^3)$ and $O((1-\sigma)^1)$ perturbative input. Fourth row:$[4/2]$, $[3/3]$, $[2/4]$ Padé approximants with $O(\sigma^3)$ and $O((1-\sigma)^2)$ perturbative input.