Classical Trace Anomaly

TL;DR

This paper explores a classical analogy to Einstein's field equations for Lovelock's equations, revealing that accepting a trace anomaly in the energy-momentum tensor is necessary, and links this anomaly to covariance properties.

Contribution

It demonstrates a classical derivation of the trace anomaly relation for second order Lagrangians, connecting it to the covariance of Einstein's equations.

Findings

Derived the trace anomaly relation for generic second order Lagrangians.

Established a classical analogy to Lovelock's equations involving trace anomalies.

Linked the existence of trace anomalies to covariance in Einstein's equations.

Abstract

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.