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

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 Shrödinger algebra. The $PT$-regularized superconformal mechanics systems in the phase of the unbroken exotic nonlinear $\mathcal{N}=4$ super-Poincaré symmetry are described by nonlinearly super-extended Schrödinger 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.

28 pages; v3: comments and references added, matches published version

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Cited by in corpus (11)

• Conformal bridge between asymptotic freedom and confinement
• Hidden symmetries of rationally deformed superconformal mechanics
• Klein four-group and Darboux duality in conformal mechanics
• Conformal bridge transformation and PT symmetry
• Hidden symmetry and (super)conformal mechanics in a monopole background
• Nonlinear supersymmetry as a hidden symmetry
• Conformal bridge in a cosmic string background
• Superfield approach to higher derivative N=1 superconformal mechanics
• Exotic nonlinear supersymmetry and integrable systems
• Hidden symmetries and nonlinear (super)algebras
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models