On Non-renormalization and OPE in Superconformal Field Theories

TL;DR

This paper investigates the operator product expansion in N=2 superconformal field theories, revealing how short multiplet conditions restrict the quantum numbers of long multiplets and explaining non-renormalization properties.

Contribution

It demonstrates that superspace shortness conditions impose strong restrictions on the quantum numbers of long multiplets, elucidating non-renormalization phenomena in superconformal theories.

Findings

No anomalous dimensions unless the third multiplet is an R-symmetry singlet

Restrictions on quantum numbers of long multiplets from short multiplet conditions

Explanation of non-renormalization of stress-tensor correlators in N=4 SYM

Abstract

The OPE of two N=2 R-symmetry current (short) multiplets is determined by the possible superspace three-point functions that two such multiplets can form with a third, a priori long multiplet. We show that the shortness conditions on the former put strong restrictions on the quantum numbers of the latter. In particular, no anomalous dimension is allowed unless the third supermultiplet is an R-symmetry singlet. This phenomenon should explain many known non-renormalization properties of correlation functions, including the one of four stress-tensor multiplets in N=4 SYM_4.