Four-point functions in N=2 superconformal field theories

TL;DR

The paper analyzes four-point functions of charge-2 hypermultiplet bilinears in N=2 superconformal field theories using two complementary frameworks: coordinate-based analytic superspace and SU(2) covariant harmonic superspace. Both approaches combine superconformal Ward identities with analyticity constraints (H-analyticity) to derive that the full four-point amplitude is determined by a single arbitrary function of the two spacetime cross-ratios (and the internal cross-ratio encoded in invariants). The authors show equivalence between the two methods, derive explicit level-1 and level-2 analyticity constraints that reduce the problem to solving a pair of first-order PDEs, and corroborate the result with a known two-loop computation in a related setup. These results provide a powerful, non-perturbative constraint on N=2 SCFT correlators and illuminate the structure of extremal and non-extremal four-point functions in harmonic superspace.

Abstract

Four-point correlation functions of hypermultiplet bilinear composites are analysed in N=2 superconformal field theory using the superconformal Ward identities and the analyticity properties of the composite operator superfields. It is shown that the complete amplitude is determined by a single arbitrary function of the two conformal cross-ratios of the space-time variables.