SUSY shields the scaling symmetry of conformal quantum mechanics
- URL: http://arxiv.org/abs/1912.13014v1
- Date: Mon, 30 Dec 2019 17:15:51 GMT
- Title: SUSY shields the scaling symmetry of conformal quantum mechanics
- Authors: A.A. Lima, J.V.S. Scursulim, U. Camara da Silva, G.M. Sotkov
- Abstract summary: 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.
We show that potentials with couplings in the strongly-repulsive and in the weak-medium ranges can be related by a dynamical supersymmetry.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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