Hidden and explicit quantum scale invariance

Abstract

There exist renormalization schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale-invariant renormalization breaks renormalizability and induces new nontrivial operators in the theory. In this work, we study the effects of such scale-invariant renormalization procedures. On the one hand, an explicitly quantum scale-invariant theory can emerge from the scale-invariant renormalization 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 renormalized with scale-dependent renormalization (such as the traditional $\overline{\mathrm{MS}}$ scheme). In this last case, scale invariance is hidden in the theory, in the sense that it only appears explicitly after renormalization.