SUSY shields the scaling symmetry of conformal quantum mechanics

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 ra...

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Bibliographic Details
Published in:arXiv.org 2019-12
Main Authors: Lima, A A, Scursulim, J V S, U Camara da Silva, Sotkov, G M
Format: Article
Language:English
Subjects:
Couplings
Critical point
Invariance
Quantum mechanics
Scaling
Subgroups
Supersymmetry
Symmetry
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1912.13014