Vacuum energy and trace anomaly

TL;DR

This paper discusses how vacuum energy and trace anomalies in quantum field theories, especially QCD, influence scale symmetry breaking and the challenges in isolating gluon condensate effects on the cosmological constant.

Contribution

It highlights the necessity of a unit operator in the trace anomaly and explains the inseparability of gluon condensate effects from vacuum energy contributions.

Findings

Vacuum energy breaks scale symmetry alongside the trace anomaly.

A unit operator is required in the trace anomaly for consistency.

Gluon condensate effects cannot be isolated from vacuum energy in QCD.

Abstract

Concerning the trace anomaly in field theory a nonvanishing vacuum energy breaks the scale symmetry as well, in addition to the usual beta function dependent term, requiring a unit operator in the trace anomaly. This additional term is also necessary in quantum chromodynamics (QCD) to cancel the inherent ambiguity in the gluon condensate. The inseparability of the gluon condensate effect from the perturbative contribution to the vacuum energy renders it impossible to isolate the gluon condensate effect on the cosmological constant.