Conformal bridge in a cosmic string background

Abstract

Hidden symmetries of non-relativistic $\mathfrak{so}(2,1)\cong \mathfrak{sl}(2,\mathbb{R})$ invariant systems in a cosmic string background are studied using the conformal bridge transformation. Geometric properties of this background are analogous to those of a conical surface with a deficiency/excess angle encoded in the "geometrical parameter" $\alpha$, determined by the linear positive/negative mass density of the string. The free particle and the harmonic oscillator on this background are shown to be related by the conformal bridge transformation. To identify the integrals of the free system, we employ a local canonical transformation that relates the model with its planar version. The conformal bridge transformation is then used to map the obtained integrals to those of the harmonic oscillator on the cone. Well-defined classical integrals in both models exist only at $\alpha =q/k$ with $q,k=1,2,\dots ,$ which for $q>1$ are higher-order generators of finite nonlinear algebras. The systems are quantized for arbitrary values of $\alpha$; however, the well-defined hidden symmetry operators associated with spectral degeneracies only exist when $\alpha$ is an integer, that reveals a quantum anomaly.

arXiv comment44 pages

References in corpus (50)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Traversable wormholes: Some simple examples
• Galilean Conformal Algebras and AdS/CFT
• The Conical Singularity And Quantum Corrections To Entropy Of Black Hole
• Black Holes and Superconformal Mechanics
• Natural Wormholes as Gravitational Lenses
• SUSY in the sky
• Black Holes and Calogero Models
• Black holes, hidden symmetries, and complete integrability
• Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
• Schr"odinger invariance and space-time symmetries
• `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Anyon wave equations and the noncommutative plane
• Superconformal mechanics, black holes, and non-linear realizations
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Non-linear finite $W$-symmetries and applications in elementary systems
• Hidden supersymmetry in quantum bosonic systems
• (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
• Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• Conformal Symmetry of Relativistic and Nonrelativistic Systems and AdS/CFT Correspondence
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• N=4 superconformal Calogero models
• Conformal mechanics in Newton-Hooke spacetime
• Hidden nonlinear supersymmetries in pure parabosonic systems
• $PT$-symmetric invisible defects and confluent Darboux-Crum transformations
• Hidden symmetry of the quantum Calogero-Moser system
• The origin of the hidden supersymmetry
• Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator
• Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions
• Quantum mechanics in curved space-time
• Five Vortex Equations
• Vacuum polarization induced by a cosmic string in anti-de Sitter spacetime
• Conformal bridge between asymptotic freedom and confinement
• From PT-symmetric quantum mechanics to conformal field theory
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• On realizations of nonlinear Lie algebras by differential operators
• On the dynamics of a particle on a cone
• Relativistic quantum dynamics of spin-0 massive charged particle in the presence of external fields in 4D curved space-time with a cosmic string
• Klein four-group and Darboux duality in conformal mechanics
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
• Hidden superconformal symmetry: Where does it come from?
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• SU(2$|$1) supersymmetric mechanics on curved spaces
• Hidden symmetry and (super)conformal mechanics in a monopole background
• Quantum Mechanics and Hidden Superconformal Symmetry

Cited by in corpus (4)

• Overspinning naked singularities in AdS${}_3$ spacetime
• Hidden symmetries from distortions of the conformal structure
• Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• Projective Time, Cayley Transformations and the Schwarzian Geometry of the Free Particle--Oscillator Correspondence