AdS/SCFT in Superspace

TL;DR

The article develops a superspace formulation of AdS/CFT for IIB on $AdS_5\times S^5$ and its boundary $D=4$, $N=4$ SCFT, using harmonic and analytic superspace to implement superconformal Ward identities. By exploiting analyticity and invariants, it proves non-renormalisation of two- and three-point functions, establishes the triviality of extremal and next-to-extremal correlators, and clarifies the structure of four-point functions and the OPE, including the appearance of the Konishi multiplet as an analytic tensor field. It also connects KK supermultiplets with boundary operators ${\rm tr}(W^p)$ and demonstrates that analytic superspace provides a consistent framework for encoding AdS/CFT data, with explicit constructions of invariants and reduction formulas guiding non-renormalisation results. Overall, the work strengthens the holographic dictionary by showing how superspace techniques yield precise constraints on correlators and OPE data in the boundary SCFT.

Abstract

A discussion of the AdS/CFT correspondence in IIB is given in a superspace context. The main emphasis is on the properties of SCFT correlators on the boundary which are studied using harmonic superspace techniques. These techniques provide the easiest way of implementing the superconformal Ward identities. The Ward identities, together with analyticity, can be used to give a compelling argument in support of the non-renormalisation theorems for two- and three-point functions, and to establish the triviality of extremal and next-to-extremal correlation functions. The OPE in is also briefly discussed.