Conformal bridge in a cosmic string background

Hidden symmetries of non-relativistic $\mathfrak{so} (2,1)\cong \mathfrak{sl}(2, {\mathbb R})$ invariant systems in a cosmic string background are studied using the conformal bridge transformation. Geometric properties this analogous to those conical surface with deficiency/excess angle encoded "geometrical parameter" $\alpha$, determined by linear positive/negative mass density string. The free particle and harmonic oscillator on shown be related To identify integrals system, we employ local canonical transformation that relates model its planar version. is then used map obtained cone. Well-defined classical both models exist only at $\alpha=q/k$ $q,k=1,2,\ldots,$ which for $q>1$ higher-order generators finite nonlinear algebras. quantized arbitrary values $\alpha$; however, well-defined hidden symmetry operators associated spectral degeneracies when $\alpha$ an integer, reveals quantum anomaly.