Construction of a Wilson action for the Wess-Zumino model

TL;DR

This paper constructs a Wilson action for the Wess-Zumino model using the exact renormalization group without superfields, demonstrating consistency via BRST formalism and revealing a quadratically divergent scalar mass term.

Contribution

It introduces a novel perturbative construction of a supersymmetric Wilson action without superfields or auxiliary fields, ensuring all-order consistency with BRST formalism.

Findings

Successfully constructs a Wilson action for the Wess-Zumino model

Demonstrates all-order consistency using BRST formalism

Identifies a quadratically divergent scalar mass term

Abstract

We construct a Wilson action for the Wess-Zumino model by applying the exact renormalization group perturbatively. Using neither superfields nor auxiliary fields, we construct a supersymmetric action only with complex scalar and Majorana spinor fields. We adopt the BRST (antifield) formalism to show the consistency of the construction to all orders in loop expansions. The resulting action has a quadratically divergent scalar mass term which is absent in the superfield formalism.