Protected Operators in N=2,4 Supersymmetric Theories

TL;DR

This paper proves that certain scalar composite operators in N=2 and N=4 supersymmetric theories have zero anomalous dimension at all perturbative orders, indicating their protected status across various models.

Contribution

It provides a general proof that scalar operators' anomalous dimensions vanish in N=2 theories with hypermultiplets, extending to N=4 and non-conformal N=2 models.

Findings

Anomalous dimensions of scalar operators vanish at all perturbative orders.

The proof applies to theories with arbitrary hypermultiplet representations.

Results confirm protected status of operators in N=2 and N=4 supersymmetric theories.

Abstract

The anomalous dimension of single and multi-trace composite operators of scalar fields is shown to vanish at all orders of the perturbative series. The proof hold for theories with N=2 supersymmetry with any number of hypermultiplets in a generic representation of the gauge group. It then applies to the finite N=4 theory as well as to non conformal N=2 models.