# Hidden and explicit quantum scale invariance

## TL;DR

This paper explores how different renormalisation schemes can preserve or hide quantum scale invariance, revealing the conditions under which scale invariance emerges explicitly or remains hidden after renormalisation.

## Contribution

It demonstrates that quantum scale invariance can be explicitly preserved or hidden depending on the renormalisation scheme used, providing new insights into scale invariance in quantum theories.

## Key findings

- Explicit scale invariant renormalisation preserves scale invariance at quantum level.
- Hidden scale invariance can emerge from traditional renormalisation schemes.
- Scale invariance can be either explicit or hidden depending on the renormalisation approach.

## Abstract

There exist renormalisation schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale invariant renormalisation breaks renormalisability and induces new non-trivial operators in the theory. In this work, we study the effects of such scale invariant renormalisation procedures. On the one hand, an explicitly quantum scale invariant theory can emerge from the scale invariant renormalisation of a scale invariant Lagrangian. On the other hand, we show how a quantum scale invariant theory can equally emerge from a Lagrangian visibly breaking scale invariance renormalised with scale dependent renormalisation (such as the traditional MS-bar scheme). In this last case, scale invariance is hidden in the theory, in the sense that it only appears explicitly after renormalisation.