$\mathcal{N}=4$ Super Yang-Mills Flux Tube in AdS

Abstract

We study a supersymmetric Wilson line on the boundary of $\mathcal{N}=4$ super Yang-Mills theory in AdS$_4$, or equivalently on a half-space, as a model for exploring the connection between holographic strings and confining flux tubes. The boundary breaks four-dimensional conformal symmetry and is expected to remove integrability, bringing this system closer to a confining string while preserving enough supersymmetry to constrain its dynamics. Working in the planar limit, we analyze the defect spectrum at weak and strong coupling and compute the superconformal index, thereby relating the perturbative gauge-theory description to the worldsheet excitations of a long holographic string. These complementary perspectives allow us to propose a map between operators in the two regimes, under which the worldsheet axion, in particular, becomes a two-particle state at strong coupling. The resulting picture supports a smooth interpolation from an exponentially growing gauge-theory spectrum to the Cardy-like spectrum of a string worldsheet, providing a non-integrable supersymmetric model for investigating the spectral reorganization expected in confining gauge theories.