Mini-Instantons

TL;DR

This paper reveals that in scale-invariant theories, inhomogeneous saddle points influence the semiclassical expansion, causing non-renormalizable operators to affect instanton effects and challenging traditional notions of universality.

Contribution

It demonstrates how non-renormalizable operators impact instanton dynamics and the beta function in two-dimensional non-linear sigma models, highlighting a non-perturbative breakdown of universality.

Findings

Instanton fugacity depends on non-renormalizable operators

Beta function varies with non-renormalizable operators

Universality concept is non-perturbatively broken

Abstract

It is shown that the inhomogeneous saddle points of scale invariant theories make the semiclassical expansion sensitive on the choice of non-renormalizable operators. In particular, the instanton fugacity and the beta function of the two dimensional non-linear sigma model depends on apparently non-renormalizable operators. This represents a non-perturbative breakdown of that concept of universality which is based on low dimensional operators.