The absence of cut--off effects for the fixed point action in 1--loop perturbation theory

TL;DR

This paper investigates whether the fixed point action in a non-linear sigma model exhibits cutoff effects at 1-loop perturbation theory, finding no such effects and supporting the idea of cutoff-independent predictions.

Contribution

The study provides the first explicit calculation showing the absence of cutoff effects for the fixed point action at 1-loop in a non-linear sigma model.

Findings

No cutoff effects of the form g^4(a/L)^n are observed.

Results support cutoff independence of physical predictions at 1-loop.

Comparison with standard and improved actions confirms the findings.

Abstract

In order to support the formal renormalization group arguments that the fixed point action of an asymptotically free model gives cut--off independent physical predictions in 1--loop perturbation theory, we calculate the finite volume mass--gap $m(L)$ in the non--linear $\sigma$--model. No cut--off effect of the type $g^4\left(a/L\right)^n$ is seen for any $n$. The results are compared with those of the standard and tree level improved Symanzik actions.