Shortening of primary operators in N-extended SCFT_4 and harmonic-superspace analyticity

TL;DR

This paper analyzes the shortening conditions of primary superfields in N-extended superconformal theories, linking harmonic superspace structures with BPS states in AdS/CFT, and explores implications for multitrace operators.

Contribution

It provides a comprehensive classification of superfield shortenings in harmonic superspace and relates them to BPS conditions and multitrace operators in AdS/CFT correspondence.

Findings

Classified all possible shortenings of primary superfields.

Connected superfield shortenings to BPS conditions in AdS/CFT.

Applied analysis to multitrace operators and supergravity states.

Abstract

We present the analysis of all possible shortenings which occur for composite gauge invariant conformal primary superfields in SU(2,2/N) invariant gauge theories. These primaries have top-spin range N/2 \leq J_{max} < N with J_{max} = J_1 + J_2, (J_1,J_2) being the SL(2,C) quantum numbers of the highest spin component of the superfield. In Harmonic superspace, analytic and chiral superfields give J_{max}= N/2 series while intermediate shortenings correspond to fusion of chiral with analytic in N=2, or analytic with different analytic structures in N=3,4. In the AdS/CFT language shortenings of UIR's correspond to all possible BPS conditions on bulk states. An application of this analysis to multitrace operators, corresponding to multiparticle supergravity states, is spelled out.