Hidden symmetries of rationally deformed superconformal mechanics

Abstract

We study the spectrum generating closed nonlinear superconformal algebra that describes $\mathcal{N}=2$ super-extensions of rationally deformed quantum harmonic oscillator and conformal mechanics models with coupling constant $g=m(m+1)$, $m\in \mathbb{N}$. It has a nature of a nonlinear finite $W$ superalgebra being generated by higher derivative integrals, and generally contains several different copies of either deformed superconformal $\mathfrak{osp}(2|2)$ algebra in the case of super-extended rationally deformed conformal mechanics models, or deformed super-Schrodinger algebra in the case of super-extension of rationally deformed harmonic oscillator systems.

40 pages, 2 figures. References added. Published version

References in corpus (15)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Physics and Mathematics of Calogero particles
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Cosmological aspects of the Eisenhart-Duval lift
• Analogue Cosmological Particle Creation: Quantum Correlations in Expanding Bose Einstein Condensates
• A Hidden Symmetry of AdS Resonances
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
• Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
• Hidden superconformal symmetry: Where does it come from?
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems

Cited by in corpus (14)

• Conformal bridge between asymptotic freedom and confinement
• Klein four-group and Darboux duality in conformal mechanics
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
• Time-dependent Dunkl-Pauli Oscillator
• Nonlinear supersymmetry as a hidden symmetry
• Superfield approach to higher derivative N=1 superconformal mechanics
• Do equidistant energy levels necessitate a harmonic potential?
• Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanics
• Exotic nonlinear supersymmetry and integrable systems
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• Hidden symmetries and nonlinear (super)algebras
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry