Study of theta-Vacua in the 2-d O(3) Model

TL;DR

This study examines how the theta parameter influences the continuum limit of the 2-d O(3) model, confirming its relevance and the predictions of the exact S-matrix theory at theta = pi, using improved computational methods.

Contribution

It demonstrates that theta is a non-perturbatively relevant parameter in the 2-d O(3) model and confirms the exact S-matrix prediction at theta = pi with high-precision data.

Findings

Different continuum values of the step scaling function for each theta

Confirmation of the S-matrix theory prediction at theta = pi

Use of improved estimators and constrained actions reduces cut-off effects

Abstract

We investigate the continuum limit of the step scaling function in the 2-d O(3) model with different theta-vacua. Since we find a different continuum value of the step scaling function for each value of theta, we can conclude that theta indeed is a relevant parameter of the theory and does not get renormalized non-perturbatively. Furthermore, we confirm the result of the conjectured exact S-matrix theory, which predicts the continuum value at theta = pi. To obtain high precision data, we use a modified Hasenbusch improved estimator and an action with an optimized constraint, which has very small cut-off effects. The optimized constraint action combines the standard action of the 2-d O(3) model with a topological action. The topological action constrains the angle between neighboring spins and is therefore invariant against small deformations of the field.