Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

Abstract

Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the equations of motion are found by employing a local canonical transformation, that leads to their natural interpretation in terms of Riemann surfaces. The cone parameter α and the angular velocity Ω of the background determine the existence of hidden symmetries. Globally defined higher order integrals associated with perihelion of geodesic orbits appear at rational values of α. For the harmonic oscillator system with frequency ω, the integrals responsible for the trajectory closure arise only for rational values of α and |γ| = |Ω/ω|, with |γ| = 1 corresponding to the Landau problem. We face a quantum anomaly problem since the hidden symmetry operators can only be constructed when α is integer. Such operators are non-local in the case of the free particle. For the harmonic oscillator, the symmetry generators are obtained with the help of the conformal bridge transformation. We also study a multi-particle version of the harmonic oscillator system with |γ| = 1 using the mean-field theory and find that the emerging vortex structure respects a singular point of the background.

Conformal bridge transformation, $$ \mathcal{PT} $$- and supersymmetry

“…The present article aims to construct supersymmetric extensions of this model on the real line and of its generalization in the Euclidean plane. The resulting systems are interesting for their connection with the spin-1/2 Landau problem, the models in the presence of Aharonov-Bohm flux associated with anyons [52][53][54][55], the physics of Bose-Einstein condensates in rotating harmonic traps [56,57], and gravitoelectromagnetism [58].…”

“…This mapping relates the symmetry generators and eigenstates of asymptotically free and harmonically confined versions of the so(2, 1) ∼ = sl(2, R) conformal mechanics models (e.g., of the free particle and the harmonic oscillator in the simplest case). In this way, we identified hidden symmetries and spectra of different harmonically trapped systems in a monopole [65] and cosmic string backgrounds [58,66], and constructed exotic rotational invariant harmonic oscillator (ERIHO) related to the physics of Bose-Einstein condensates [57] and gravitoelectromagnetism [58]. The CBT was also applied to the study of the black holes mechanics in ref.…”

“…In this context, one may wonder what forms the symmetries and supersymmetries of models like those discussed in the last section will take if we modify the space-time. For example, one can study the case of conical geometry, which formally can be obtained from our Hermitian systems (4.45) and (4.83) via the local canonical transformation [58,66]…”

Klein–Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies

“…Its compact form allowed analytical research studies of many physical and mathematical systems in gravitational backgrounds with rotation and causality violation. It has been shown that all spacetime homogeneous (ST-homogeneous) Gö del-type metrics characterized by the vorticity Ω of spacetime (a real number that is related to rotation of the material, i.e., | | W =  W [8]) and a given value of the parameter ˜m m -¥ ¥   ; 2 , can be transformed in cylindrical coordinates [8][9][10][11][12][13][14][15][16][17][18] to Here, the disclination parameter α (curvature parameter) admits the values 0 < α < 1 in general relativity (for cosmic strings with positive curvature), α > 1 in the geometric theory of defects in condensed matter (for a negative curvature), and Ω = 0 and α = 1 corresponds to Minkowski flat spacetime metric. Moreover, for m < 0 2 there is an infinite number of successive causal and noncausal regions, and for m < W  0 2 2 there is one noncausal region for a given r > r c .…”

“…Moreover, the covariant and contravariant metric tensors associated with the Som-Raychaudhuri spacetime are, respectively, given by The objective of the current methodical proposal is to explore in a comprehensive manner the effect of the gravitational field generated by the Gödel-type cosmic string SR-spacetime equation (2) on the spectra of some Klein-Gordon (KG) particles of fundamental quantum gravity nature, like the KG-oscillators and KG-Coulomb models. Such fundamental models have been studied by different authors (e.g., [12][13][14][15][16][17][18][22][23][24]) where the vorticity parameter Ω is assumed to take the form Ω 0 and the energies are assumed to be positive…”