Minimal Surfaces of the $Ad{S}_5\times S^5$ Superstring and the Symmetries of Super Wilson Loops at Strong Coupling

Based on an extension of the holographic principle to superspace, we provide a strong-coupling description of smooth super Wilson loops in terms of minimal surfaces of the $Ad{S}_5\times S^5$ superstring. We employ the classical integrability of the Green-Schwarz superstring on $Ad{S}_5\times S^5$ to derive the superconformal and Yangian $Y[\mathfrak{p}\mathfrak{s}\mathfrak{u}(2,2\mathrm{\mid }4)]$ Ward identities for the super Wilson loop, thus extending the strong coupling results obtained for the Maldacena-Wilson loop. In the course of the derivation, we determine the minimal surface solution up to third order in an expansion close to the conformal boundary.