Transmuted spectrum-generating algebras and detectable parastatistics of the Superconformal Quantum Mechanics

Abstract: In a paper (Balbino-de Freitas-Rana-FT, arXiv:2309.00965) we proved that the supercharges of the supersymmetric quantum mechanics can be statistically transmuted and accommodated into a $Z_2^n$-graded parastatistics. In this talk I derive the $6=1+2+3$ transmuted spectrum-generating algebras (whose respective $Z_2^n$ gradings are $n=0,1,2$) of the ${\cal N}=2$ Superconformal Quantum Mechanics. These spectrum-generating algebras allow to compute, in the corresponding multiparticle sectors of the de Alfaro-Fubini-Furlan deformed oscillator, the degeneracies of each energy level. The levels induced by the $Z_2\times Z_2$-graded paraparticles cannot be reproduced by the ordinary bosons/fermions statistics. This implies the theoretical detectability of the $Z_2\times Z_2$-graded parastatistics.