A note on the torque anomaly

TL;DR

This paper investigates the torque anomaly in conical geometries, reproduces previous findings, and demonstrates a mathematical cancellation of the anomaly through a variational approach and geometric truncation.

Contribution

It provides a detailed analysis of the torque anomaly in conical geometries and shows how to mathematically cancel it using a variational method and geometric truncation.

Findings

Reproduction of the torque anomaly in conical geometries.

Identification of a mathematical cancellation mechanism for the anomaly.

Insight into the role of geometric truncation in anomaly cancellation.

Abstract

I reproduce, in the case of a conical geometry, the torque anomaly recently noted by Fulling, Mera and Trendafilova for the wedge. The expected conservation equation is obtained by a variational method and a mathematical cancellation of the anomaly is exhibited, motivated by the process of truncating the cone at some inner radius.