Hidden superconformal symmetry: Where does it come from?

2019

Phys. Rev. D

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We study the spectrum generating closed nonlinear superconformal algebra that describes N = 2 super-extensions of rationally deformed quantum harmonic oscillator and conformal mechanics models with coupling constant g = m(m + 1), m ∈ 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 osp(2|2) algebra in the case of superextended rationally deformed conformal mechanics models, or deformed super-Schrödinger algebra in the case of super-extension of rationally deformed harmonic oscillator systems.

Section: Osp(2|2) and Super-schrödinger Symmetriessupporting

confidence: 75%

Hidden symmetries of rationally deformed superconformal mechanics

Inzunza

2019

Phys. Rev. D

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“…The peculiarity of supersymmetric parabosonic systems shows up in the nonlocal nature of supercharges to be of infinite order in the momentum operator as well as in the ladder operators but anti-commuting for a polynomial in Hamiltonian being quadratic in creation-annihilation operators. Similar peculiarities characterize hidden supersymmetry and hidden superconformal symmetry appearing in some usual quantum bosonic systems with a local Hamiltonian operator [46,47,48,20,21,24,25,26,30,31,32,35,49,50,51]. Exotic supersymmetry emerges in superextensions of the quantum systems described by soliton and finite-gap potentials, in which the key role is played by the Lax-Novikov integrals of motion [30,31,32,33,42].…”

Section: Introductionmentioning

confidence: 84%

Nonlinear Supersymmetry as a Hidden Symmetry

Integrability, Supersymmetry and Coherent States

2019

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Nonlinear supersymmetry is characterized by supercharges to be higher order in bosonic momenta of a system, and thus has a nature of a hidden symmetry. We review some aspects of nonlinear supersymmetry and related to it exotic supersymmetry and nonlinear superconformal symmetry. Examples of reflectionless, finite-gap and perfectly invisible PT -symmetric zero-gap systems, as well as rational deformations of the quantum harmonic oscillator and conformal mechanics, are considered, in which such symmetries are realized.

“…The (anti)-commutators not displayed here do vanish. This superalgebra is identified as the osp(2|2) superconformal symmetry which appears in systems like one-dimensional harmonic super-oscillator or the superconformal mechanics model with a confining term [65,16,17,63]. Therefore our construction maybe considered as generalization of the three-dimensional versions of these systems in the monopole background.…”

Section: The Osp(2|2) Superconformal Extensionmentioning

confidence: 99%

Hidden symmetry and (super)conformal mechanics in a monopole background

Inzunza

Wipf

2020

J. High Energ. Phys.

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We study classical and quantum hidden symmetries of a particle with electric charge e in the background of a Dirac monopole of magnetic charge g subjected to an additional central potential V (r) = U (r) + (eg) 2 /2mr 2 with U (r) = 1 2 mω 2 r 2 , similar to that in the one-dimensional conformal mechanics model of de Alfaro, Fubini and Furlan (AFF). By means of a non-unitary conformal bridge transformation, we establish a relation of the quantum states and of all symmetries of the system with those of the system without harmonic trap, U (r) = 0. Introducing spin degrees of freedom via a very special spin-orbit coupling, we construct the osp(2|2) superconformal extension of the system with unbroken N = 2 Poincaré supersymmetry and show that two different superconformal extensions of the one-dimensional AFF model with unbroken and spontaneously broken supersymmetry have a common origin. We also show a universal relationship between the dynamics of a Euclidean particle in an arbitrary central potential U (r) and the dynamics of a charged particle in a monopole background subjected to the potential V (r).To solve the vector equation in (2.4) in the case J 2 > ν 2 , which we will assume in what follows, we decompose n into the component parallel to the angular momentum and the orthogonal component,whereĴ is the unit vector in the direction of J . Since the parallel component n is constant, we conclude that the orthogonal component n ⊥ (t) has constant length and thus describes a circle in the plane orthogonal to J , n ⊥ (t) = n ⊥ (0) cos ϕ(t) +Ĵ × n ⊥ (0) sin ϕ(t) .(2.15) Here, θ, ϕ and ψ are the Euler angles, 0 ≤ ϕ, ψ < 2π, 0 ≤ θ < π, and J i J i = K a K a = J 2 . The common eigenstates of J 2 , J 3 and K 3 satisfying relations