Supercurrent, Supervirial and Superimprovement

TL;DR

This paper explores the structure of supercurrent supermultiplets in supersymmetric theories, highlighting the independence of R-symmetry and dilatation symmetry, and introduces novel scale-invariant trajectories in non-unitary models.

Contribution

It characterizes the Virial multiplet for general supersymmetric theories and presents new scale-invariant trajectories with nilpotent coupling constants.

Findings

Dilatation symmetry is manifest in the Virial multiplet.

R-symmetry and dilatation symmetry are independent.

Novel scale-invariant trajectories in non-unitary models.

Abstract

Supersymmetric field theories possess a rich structure in their supercurrent supermultiplets. Some symmetries are manifest in one supercurrent supermultiplet but not in the others; for instance, R-symmetry is manifest in the R-multiplet but not in the Ferrara-Zumino multiplet. Similarly, we argue that dilatation symmetry is manifest in the Virial multiplet (also known as a variant minimal supercurrent supermultiplet in the literature). It reveals that R-symmetry and dilatation symmetry are conceptually independent without further assumptions even though the superconformal symmetry connects the two. We show the structure of the Virial multiplet for general renormalizable supersymmetric field theories in (1+3) dimension to all orders in perturbation theory, and discuss the condition for the dilatation invariance (but not necessarily R-symmetric nor superconformal). We present novel scale invariant trajectories with a nilpotent structure in coupling constants for non-unitary Wess-Zumino models with non-vanishing beta functions, which are, therefore, not superconformal.