Symmetries of the Boundary of AdS_5 x S^5 and Harmonic Superspace

TL;DR

This paper explores how the symmetries of AdS_5 x S^5 manifest on its boundary, relating bulk isometries to boundary superconformal symmetry and harmonic superspace, with implications for N=2 super Yang-Mills theory.

Contribution

It establishes a connection between bulk AdS symmetries and boundary harmonic superspace, specifically relating the S^2 submanifold of S^5 to N=2 harmonic superspace structures.

Findings

Boundary superconformal symmetry realized on boundary coordinates and harmonics.

Identification of the S^2 submanifold of S^5 with the harmonic space of N=2 supersymmetry.

Relation between bulk isometries and boundary off-shell superspace coordinates.

Abstract

We study the boundary limit of the bulk isometries of AdS x S. The superconformal symmetry is realized on the coordinates of the AdS boundary, the fermionic superspace coordinates, and the harmonics on the sphere. We show how these may be related to the coordinates of an off-shell harmonic superspace of SCFT living on the boundary. In the special case of d=4, N=2 super Yang-Mills theory, a truncation of the N=4 SYM dual to Type IIB string theory compactified on AdS_5 x S^5, we identify the bosonic space SU(2)/U(1) of the N=2 harmonic superspace (known before as auxiliary) with the S^2 submanifold of the S^5.