The Hierarchical $\phi^4$ - Trajectory by Perturbation Theory in a Running Coupling and its Logarithm

TL;DR

This paper develops a perturbative approach to the hierarchical 4-trajectory using a running coupling, addressing singularities in three dimensions, and analyzing eigenvalues and fusion rules.

Contribution

It introduces a novel perturbation theory framework for the hierarchical 4-trajectory with a running coupling, resolving singularities and computing eigenvalues and fusion rules.

Findings

Resolved singularities via logarithms of the running coupling

Numerical data supporting the theoretical framework

Computed eigenvalues and fusion rules along the trajectory

Abstract

We compute the hierarchical $\phi^4$-trajectory in terms of perturbation theory in a running coupling. In the three dimensional case we resolve a singularity due to resonance of power counting factors in terms of logarithms of the running coupling. Numerical data is presented and the limits of validity explored. We also compute moving eigenvalues and eigenvectors on the trajectory as well as their fusion rules.