Bulk Gauge Fields in AdS Supergravity and Supersingletons

TL;DR

This paper explores the relationship between boundary conformal operators and bulk fields in AdS supergravity, classifying various supermultiplets and their contributions to correlation functions, with implications for string theory corrections.

Contribution

It provides a comprehensive description of conformal operators, supermultiplets, and their roles in AdS/CFT correspondence, including contributions to OPE and Green's functions.

Findings

Classification of conformal operators at unitarity bounds

Identification of supermultiplets with KK and string states

Formulation of contributions to correlation functions

Abstract

We describe conformal operators living at the boundary of $AdS_{d+1}$ in a general setting. Primary conformal operators at the threshold of the unitarity bounds of UIR's of O(d,2) correspond to singletons and massless fields in $AdS_{d+1}$, respectively. For maximal supersymmetric theories in $AdS_{d+1}$ we describe ``chiral'' primary short supermultiplets and non-chiral primary long supermultiplets. Examples are exhibited which correspond to KK and string states. We give the general contribution of a primary conformal operator to the OPE and Green's functions of primary fields, which may be relevant to compute string corrections to the four-point supergraviton amplitude in Anti-de-Sitter space. The material in this paper was presented by one of the authors (S.F) at String 98, Santa Barbara.