Holography in Superspace

TL;DR

This work extends the AdS/CFT correspondence to superspace by formulating bulk–boundary holography in terms of coset supermanifolds, showing that the $(10|32)$ AdS$_5\times S^5$ bulk and the $(10|16)$ boundary conformal superspace share boundary-compatible symmetries with half the bulk fermions decoupling. It defines a supersymmetric Wilson loop in ${\cal N}=4$ SYM and proves its quantum κ-invariance for lightlike, smooth loops on-shell, identifying this invariance with the κ-invariance of the corresponding string worldsheet in $AdS_5\times S^5$ via boundary conditions. The analysis shows a precise boundary mapping where $X^\mu$ is fixed, $Y^m$ satisfies Neumann conditions, and $\theta=\lambda$ on the boundary, with the Virasoro constraint at the boundary equivalent to $p^2=0$. However, κ-invariance is broken at loop self-intersections, offering a potential link to loop equations in the superspace context. Overall, the paper provides a concrete holographic bridge between bulk string κ-symmetry and boundary gauge theory κ-symmetry, illuminating how supersymmetric Wilson loops encode bulk–boundary dynamics.

Abstract

The AdS/CFT correspondence identifies the coordinates of the conformal boundary of anti-de Sitter space with the coordinates of the conformal field theory. We generalize this identification to theories formulated in superspace. As an application of our results, we study a class of Wilson loops in N=4 SYM theory. A gauge theory computation shows that the expectation values of these loops are invariant under a local kappa-symmetry, except at intersections. We identify this with the kappa-invariance of the associated string worldsheets in the corresponding bulk superspace.