Hidden symmetries of rationally deformed superconformal mechanics

TL;DR

This paper explores the complex nonlinear superconformal algebra underlying rationally deformed quantum harmonic oscillator and conformal mechanics models with specific coupling constants, revealing hidden symmetries and algebraic structures.

Contribution

It identifies and analyzes the nonlinear finite W superalgebra structure in super-extended rationally deformed models, uncovering multiple copies of deformed superconformal and super-Schrodinger algebras.

Findings

The superalgebra is generated by higher derivative integrals.

Multiple copies of deformed superconformal and super-Schrodinger algebras are present.

The algebraic structure is a nonlinear finite W superalgebra.

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.