Spontaneously Broken Conformal Symmetry: Dealing with the Trace Anomaly

TL;DR

This paper explores how to maintain conformal symmetry at the quantum level in non-renormalizable theories by constructing models where the trace anomaly is avoided, demonstrated through explicit one-loop computations.

Contribution

It introduces a method to preserve scale and conformal invariance in quantum theories by discarding renormalizability and provides explicit models with traceless energy-momentum tensors.

Findings

Explicit one-loop computations show preserved conformal invariance.

Constructed models have traceless energy-momentum tensors.

Demonstrated viability of non-renormalizable, conformally invariant models.

Abstract

The majority of renormalizable field theories possessing the scale invariance at the classical level exhibits the trace anomaly once quantum corrections are taken into account. This leads to the breaking of scale and conformal invariance. At the same time any realistic theory must contain gravity and is thus non-renormalizable. We show that discarding the renormalizability it is possible to construct viable models allowing to preserve the scale invariance at the quantum level. We present explicit one-loop computations for two toy models to demonstrate the main idea of the approach. Constructing the renormalized energy momentum tensor we show that it is traceless, meaning that the conformal invariance is also preserved.