Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case

TL;DR

This paper investigates the 2D O(3) model at theta near pi as a simplified test case for understanding walking behavior near a conformal fixed point, relevant for nonperturbative studies of technicolor models.

Contribution

It demonstrates how the 2D O(3) model can serve as a toy model to study walking near a conformal fixed point through numerical simulations of the running coupling and finite size scaling.

Findings

Observed walking behavior in the beta-function near the conformal point

Finite size scaling analysis of the mass gap supports conformal dynamics

Numerical results align with theoretical expectations for walking near a fixed point

Abstract

Slowly walking technicolor models provide a mechanism for electroweak symmetry breaking whose nonperturbative lattice investigation is rather challenging. Here we demonstrate walking near a conformal fixed point considering the 2-d lattice O(3) model at vacuum angle $\theta \approx \pi$. The essential features of walking technicolor models are shared by this toy model and can be accurately investigated by numerical simulations. We show results for the running coupling and the beta-function and we perform a finite size scaling analysis of the massgap close to the conformal point.