Halpern-Huang directions in effective scalar field theory

TL;DR

This paper demonstrates that the relevant directions identified by Halpern and Huang in scalar field theory can be derived from Polchinski's Wilson renormalization group, confirming their cutoff independence.

Contribution

It provides a derivation of Halpern and Huang's results using Polchinski's RG, establishing cutoff function independence.

Findings

Relevant directions exist at the Gaussian fixed point.

Derivation confirms cutoff independence of these directions.

Supports the robustness of Halpern and Huang's findings.

Abstract

Halpern and Huang recently showed that there are relevant directions in the space of interactions at the Gaussian fixed point. I show that their result can be derived from Polchinski's form of the Wilson renormalization group. The derivation shows that the existence of these directions is independent of the cutoff function used.