On classicalization in nonlinear sigma models

TL;DR

This paper investigates classicalization in nonlinear sigma models, revealing weak and strong forms depending on derivatives and curvature, and discusses their relation to asymptotic safety and the classical limit.

Contribution

It demonstrates that nonlinear sigma models exhibit both weak and strong classicalization phenomena, with the latter being independent of curvature sign and potentially linked to asymptotic safety.

Findings

Weak classicalization occurs in two-derivative models, influenced by curvature sign.

Strong classicalization appears in models with higher derivatives, regardless of curvature.

Discussion of ambiguities in defining the classical limit.

Abstract

We consider the phenomenon of classicalization in nonlinear sigma models with both positive and negative target space curvature and with any number of derivatives. We find that the theories with only two derivatives exhibit a weak form of classicalization, and that the quantitative results depend on the sign of the curvature. Nonlinear sigma models with higher derivatives show a strong form of the phenomenon which is independent of the sign of curvature. We argue that weak classicalization may actually be equivalent to asymptotic safety, whereas strong classicalization seems to be a genuinely different phenomenon. We also discuss possible ambiguities in the definition of the classical limit.