# Trace anomaly and invariance under transformation of units

## TL;DR

This paper explores how the trace anomaly in quantum field theory signals the breaking of conformal invariance in gravitational backgrounds, emphasizing the role of units transformation invariance in quantum matter theories.

## Contribution

It demonstrates that the trace anomaly indicates the breakdown of conformal invariance of the background spacetime in the context of quantum fields and units transformation invariance.

## Key findings

- Trace anomaly signals broken conformal invariance in gravity
- Conformal invariance of quantum fields relates to units transformation invariance
- Background conformal symmetry breaking is linked to trace anomaly

## Abstract

Paying attention to conformal invariance as the invariance under local transformations of units of measure, we take a conformal invariant quantum field as a quantum matter theory in which one has the freedom to choose the values of units of mass, length and time arbitrarily at each point. To be able to have this view, it is necessary that the background on which the quantum field is based be conformal invariant as well. Consequently, defining the unambiguous expectation value of the energy-momentum tensor of such a quantum field through the Wald renormalizing prescription necessitates breaking down the conformal symmetry of the background. Then, noticing the field equations suitable for describing the back-reaction effect, we show that the existence of trace anomaly, known for indicating the brokenness of conformal symmetry in quantum field theory, can also indicate the above gravitational conformal symmetry brokenness