No Conformal Anomaly in Unimodular Gravity

TL;DR

This paper demonstrates that unimodular gravity maintains conformal invariance at the quantum level, even with conformal matter, suggesting it is a consistent truncation of Einstein-Hilbert theory.

Contribution

It shows that unimodular gravity's conformal invariance persists quantum mechanically, clarifying its relation to the full Einstein-Hilbert action and functional integral.

Findings

Conformal invariance survives quantum corrections in unimodular gravity.

Unimodular gravity can be viewed as a truncation of Einstein-Hilbert theory.

The restriction in the functional integral is consistent.

Abstract

The conformal invariance of unimodular gravity survives quantum corrections, even in the presence of conformal matter. Unimodular gravity can actually be understood as a certain truncation of the full Einstein-Hilbert theory, where in the Einstein frame the metric tensor enjoys unit determinant. Our result is compatible with the idea that the corresponding restriction in the functional integral is consistent as well.