Renormalization of supersymmetric chiral theories in rational spacetime dimensions

TL;DR

This paper investigates the renormalization of supersymmetric chiral theories with odd superpotentials in rational spacetime dimensions, revealing emergent symmetries at fixed points beyond previous non-supersymmetric results.

Contribution

It extends the renormalization analysis of supersymmetric models with odd superpotentials to higher loop orders and rational dimensions, demonstrating emergent symmetries similar to non-supersymmetric cases.

Findings

Models are renormalizable in rational spacetime dimensions.

Emergent $OSp(1|n-1)$ symmetry at fixed points.

Results extend previous non-supersymmetric findings to higher loop orders.

Abstract

We renormalize models with scalar chiral superfields with an odd superpotential to several orders in perturbation theory. These extensions of the cubic Wess-Zumino model are renormalizable in spacetime dimensions which are rational. When endowed with an $O(N)$ symmetry it is shown that they share the same property as their non-supersymmetric counterparts in that at a particular fixed point there is an emergent $OSp(1|n-1)$ symmetry, where $n$ is the power of the superpotential. This is shown at a loop order beyond that for which it was established in the parallel non-supersymmetric theory.