Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems

TL;DR

This paper explores how the Lax-Novikov integral influences the nonlinear symmetries of $PT$-regularized conformal and superconformal mechanics, revealing extended algebraic structures and symmetry breaking phenomena.

Contribution

It uncovers the nonlinear extensions of conformal and superconformal symmetries induced by the Lax-Novikov integral in $PT$-regularized systems, including new algebraic structures.

Findings

Expansion of conformal symmetry leads to a nonlinear generalized Schrödinger algebra.

Superconformal systems exhibit a nonlinear super-extended Schrödinger algebra with $osp(2|2)$ subalgebra.

In broken phases, the $osp(2|2)$ subalgebra is absent and scaling dimensions are indefinite.

Abstract

We investigate how the Lax-Novikov integral in the perfectly invisible $PT$-regularized zero-gap quantum conformal and superconformal mechanics systems affects on their (super)-conformal symmetries. We show that the expansion of the conformal symmetry with this integral results in a nonlinearly extended generalized Shr\"odinger algebra. The $PT$-regularized superconformal mechanics systems in the phase of the unbroken exotic nonlinear $\mathcal{N}=4$ super-Poincar\'e symmetry are described by nonlinearly super-extended Schr\"odinger algebra with the $osp(2|2)$ sub-superalgebra. In the partially broken phase, the scaling dimension of all odd integrals is indefinite, and the $osp(2|2)$ is not contained as a sub-superalgebra.