Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories

TL;DR

This paper proves the renormalizability of four-dimensional ${ m N}=1/2$ supersymmetric field theories using a Wilsonian approach, leveraging non-hermiticity to assign noncanonical scaling dimensions, and shows stability under soft-breaking terms.

Contribution

It provides a Wilsonian proof of renormalizability for ${ m N}=1/2$ supersymmetric theories by exploiting non-hermiticity and noncanonical scaling dimensions.

Findings

Renormalizability proven via power counting with noncanonical dimensions.

Stability of renormalizability under soft-breaking terms.

Some soft-breaking terms become marginal with new scaling assignments.

Abstract

We provide Wilsonian proof for renormalizability of four-dimensional quantum field theories with ${\cal N}=1/2$ supersymmetry. We argue that the non-hermiticity inherent to these theories permits assigning noncanonical scaling dimension both for the Grassman coordinates and superfields. This reassignment can be done in such a way that the non(anti)commutativity parameter is dimensionless, and then the rest of the proof ammounts to power counting. The renormalizability is also stable against adding standard four-dimensional soft-breaking terms to the theory. However, with the new scaling dimension assignments, some of these terms are not just relevant deformations of the theory but become marginal.