Multiband models for field theories with anomalous current dimension

TL;DR

This paper presents simple quantum mechanical models demonstrating scale invariance with anomalous current dimensions, highlighting how such symmetries can be approximate at finite N and exact in large N limits.

Contribution

It introduces minimal models showing anomalous current dimensions and explores the emergence of scale invariance as an approximate symmetry at finite N.

Findings

Scale invariance with anomalous current dimension in simple models

Approximate symmetry persists at finite N

Exact symmetry emerges in large N limit

Abstract

We give simple examples of weakly coupled or free quantum mechanical systems that exhibit scale invariance with an anomalous dimension for a conserved current. In these models scaling as an exact symmetry only emerges in a large N limit, but it remains as an approximate symmetry even at finite N.