Anomaly in conformal quantum mechanics: From molecular physics to black holes

TL;DR

This paper explores the conformal invariance in various physical systems, from molecular physics to black holes, highlighting the occurrence of quantum anomalies that break the symmetry in strong-coupling regimes.

Contribution

It provides a unified analysis of conformal invariance and quantum anomalies across diverse systems, emphasizing the independence from renormalization procedures.

Findings

Identification of conformal invariance in systems with inverse square potential

Demonstration of quantum symmetry breaking in strong-coupling regimes

Independence of anomaly from renormalization process

Abstract

A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular range of distances, they are characterized by a long-range conformal interaction (inverse square potential), the absence of dimensional scales, and an SO(2,1) symmetry algebra. Examples from molecular physics to black holes are provided and discussed within a unified treatment. When such systems are physically realized in the appropriate strong-coupling regime,the occurrence of quantum symmetry breaking is possible. This anomaly is revealed by the failure of the symmetry generators to close the algebra in a manner shown to be independent of the renormalization procedure.