Non-renormalization theorems without supergraphs: The Wess-Zumino model

TL;DR

This paper presents an algebraic approach to derive non-renormalization theorems for the Wess-Zumino model without using supergraph techniques, applicable to both massive and massless cases.

Contribution

It introduces a novel algebraic method based on supersymmetry variations to establish non-renormalization theorems without supergraphs.

Findings

Valid for massive and massless models

Relates chiral Green functions to convergent functions

Does not depend on superpotential properties at zero momentum

Abstract

The non-renormalization theorems of chiral vertex functions are derived on the basis of an algebraic analysis. The property, that the interaction vertex is a second supersymmetry variation of a lower dimensional field monomial, is used to relate chiral Green functions to superficially convergent Green functions by extracting the two supersymmetry variations from an internal vertex and transforming them to derivatives acting on external legs. The analysis is valid in the massive as well as in the massless model and can be performed irrespective of properties of the superpotential at vanishing momentum.