A diffeomorphism anomaly in every dimension

TL;DR

This paper demonstrates that diffeomorphism anomalies can occur in any dimension through a simple example, challenging the conventional understanding that such anomalies only exist in specific dimensions.

Contribution

It introduces a higher-dimensional generalization of the Virasoro algebra arising from canonical quantization, showing anomalies beyond traditional field-theoretic constraints.

Findings

Diffeomorphism anomalies can exist in all dimensions.

A higher-dimensional Virasoro algebra generalization is constructed.

Canonical quantization can produce anomalies in non-field-theoretic systems.

Abstract

Field-theoretic pure gravitational anomalies only exist in $4k+2$ dimensions. However, canonical quantization of non-field-theoretic systems may give rise to diffeomorphism anomalies in any number of dimensions. I present a simple example, where a higher-dimensional generalization of the Virasoro algebra arises upon quantization.