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arXiv · 1912.13014

SUSY shields the scaling symmetry of conformal quantum mechanics

A. A. Lima·J. V. S. Scursulim·U. Camara da Silva·G. M. Sotkov
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Abstract

Renormalization of the inverse square potential usually breaks its classical conformal invariance. In a strongly attractive potential, the scaling symmetry is broken to a discrete subgroup while, in a strongly repulsive potential, it is preserved at quantum level. In the intermediate, weak-medium range of the coupling, an anomalous length scale appears due to a flow of the renormalization group away from a critical point. We show that potentials with couplings in the strongly-repulsive and in the weak-medium ranges can be related by a dynamical supersymmetry. Imposing SUSY invariance unifies these two ranges, and fixes the anomalous scale to zero, thus restoring the continuous scaling symmetry.

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A. A. Lima, J. V. S. Scursulim, U. Camara da Silva, G. M. Sotkov. 2019-12-30. SUSY shields the scaling symmetry of conformal quantum mechanics. https://doi.org/10.1103/physreva.101.032105

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