Holomorphic Anomalies and the Nonrenormalization Theorem

TL;DR

This paper demonstrates that the superpotential remains unrenormalized at all perturbative orders even with massless particles, reaffirming its reliability for studying the low-energy moduli space in supersymmetric theories.

Contribution

It provides a proof that the superpotential does not receive perturbative corrections in the presence of massless particles, supporting the nonrenormalization theorem.

Findings

Superpotential is not renormalized at any perturbative order.

Confirms the utility of the Wilsonian superpotential in low-energy analysis.

Supports the nonrenormalization theorem in supersymmetric theories.

Abstract

It has been argued that the superpotential can be renormalized in the presence of massless particles. Possible implications which have been considered include the restoration of supersymmetry at higher loops or a shift to a supersymmetric vacuum state. We argue that even in the presence of massless particles, there are no new contributions to the superpotential at any order in perturbation theory. This confirms the utility of the Wilsonian superpotential for analyzing the moduli space of the low energy theory.