Holography in Superspace

TL;DR

This paper extends the holographic principle to superspace, analyzing Wilson loops in N=4 SYM theory and demonstrating their invariance under kappa-symmetry, linking gauge theory and string worldsheet symmetries.

Contribution

It generalizes the AdS/CFT correspondence to superspace and connects gauge theory Wilson loops with string worldsheet kappa-symmetry.

Findings

Wilson loop expectation values are kappa-symmetric except at intersections

Kappa-invariance of string worldsheets corresponds to gauge theory invariance

Superspace formulation unifies boundary and bulk symmetries

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.