Anomalous dimensions of twist-2 conformal operators in supersymmetric Wess-Zumino model

TL;DR

This paper investigates the scale behavior of twist-2 conformal operators in the supersymmetric Wess-Zumino model, providing analytical solutions for fermionic operators and methods to derive bosonic operators and anomalous dimensions.

Contribution

It demonstrates that multiplicatively renormalized operators can be constructed from a single supermultiplet member and offers a closed-form solution for fermionic operators.

Findings

Analytical solution for fermionic conformal operators

Method to derive bosonic operators via supersymmetry

Complete reconstruction of anomalous dimensions matrix

Abstract

We are studying scale properties of twist-2 conformal operators in supersymmetric Wess-Zumino model. In particular, we are interested in a construction of multiplicatively renormalized conformal operators. We show, that in order to find multiplicatively renormalized operators in this model, it is sufficient to find multiplicatively renormalized operators only for one member of operator supermultiplet. We found a closed analytical solution for fermionic conformal operator, which together with supersymmetry transformations could be used to find remained multiplicatively renormalized bosonic operators. Moreover, we found, that the knowledge of fermionic diagonal and non-diagonal anomalous dimensions matrices allows us completely reconstruct the forward anomalous dimensions matrix in singlet case.