SO(2,1) conformal anomaly: Beyond contact interactions

TL;DR

This paper demonstrates that conformal anomalies in SO(2,1) symmetry extend beyond contact interactions, showing their generic presence in conformal quantum mechanics and linking their origin to ultraviolet divergences.

Contribution

It reveals the existence of conformal anomalies in a broader class of systems, beyond contact interactions, and connects their emergence to ultraviolet behavior via renormalization.

Findings

Conformal anomalies occur in the two-dimensional inverse square potential.

Anomalies are linked to ultraviolet divergences in the theory.

The results suggest anomalies are a general feature of conformal quantum mechanics.

Abstract

The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity.