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

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.

11 pages. A few typos corrected in the final version

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• RG limit cycles
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• Bessel Process and Conformal Quantum Mechanics
• Multichannel Framework for Singular Quantum Mechanics
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• Inequivalent quantization in the field of a ferromagnetic wire
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• Analytic Structure of the S-Matrix for Singular Quantum Mechanics