Superconformal mechanics

Abstract

We survey the salient features and problems of conformal and superconformal mechanics and portray some of its developments over the past decade. Both classical and quantum issues of single- and multiparticle systems are covered.

1+68 pages, invited review for Journal of Physics A; v2: revised text extended by 4 pages and 11 references, published version

References in corpus (21)

• Physics and Mathematics of Calogero particles
• A classification of near-horizon geometries of extremal vacuum black holes
• Supersymmetric Calogero models by gauging
• N=4 superconformal Calogero models
• Hierarchy of N=8 Mechanics Models
• Calogero models and nonlocal conformal transformations
• N=4 mechanics, WDVV equations and roots
• Gauging N=4 supersymmetric mechanics II: (1,4,3) models from the (4,4,0) ones
• N=4 supersymmetric 3-particles Calogero model
• D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics
• Particle dynamics on AdS_2 x S^2 background with two-form flux
• New Model of N=8 Superconformal Mechanics
• Biharmonic Superspace for N=4 Mechanics
• Lobachevsky geometry of (super)conformal mechanics
• Conformal mechanics inspired by extremal black holes in d=4
• Harmonic N=2 Mechanics
• The Common Origin of Linear and Nonlinear Chiral Multiplets in N=4 Mechanics
• N=4 Multi-Particle Mechanics, WDVV Equation and Roots
• On the geometry of V-systems
• N=4 Superconformal Mechanics and Black Holes
• Harmonic Superfields in N=4 Supersymmetric Quantum Mechanics

Cited by in corpus (66)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the classical theory
• Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator
• $\mathcal{N}$-Extension of duble-graded supersymmetric and superconformal quantum mechanics
• Gauge Fields, Nonlinear Realizations, Supersymmetry
• On dynamical realizations of l-conformal Galilei groups
• Super Kähler oscillator from SU(2|1) superspace
• Superconformal mechanics in SU(2|1) superspace
• Conformal bridge between asymptotic freedom and confinement
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• $\mathcal{N}$-extended supersymmetric Calogero models
• Four types of (super)conformal mechanics: D-module reps and invariant actions
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Rational deformations of conformal mechanics
• From worldline to quantum superconformal mechanics with/without oscillatorial terms: $D(2,1;\alpha )$ and $sl(2|1)$ models
• Gauged spinning models with deformed supersymmetry
• New potentials for conformal mechanics
• SU(2|2) supersymmetric mechanics
• Hidden symmetries of rationally deformed superconformal mechanics
• Klein four-group and Darboux duality in conformal mechanics
• Extended supersymmetric Calogero model
• SU(2|1) mechanics and harmonic superspace
• Membrane Quantum Mechanics
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
• Conformal generation of an exotic rotationally invariant harmonic oscillator
• Implications of Conformal Symmetry in Quantum Mechanics
• Long multiplets in supersymmetric mechanics
• Superconformal mechanics of AdS${}_2$ D-brane boundstates
• Taming the zoo of supersymmetric quantum mechanical models
• Note on correlation functions in conformal quantum mechanics
• A classification of lowest weight irreducible modules over ${\mathbb{Z}}_2^2$-graded extension of $osp(1|2)$
• Deformed supersymmetric quantum mechanics with spin variables
• Inequivalent $Z_2^n$-graded brackets, $n$-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics
• Superconformal quantum mechanics and the exterior algebra
• Minimal unitary representation of D(2,1;λ) and its SU(2) deformations and d=1, N=4 superconformal models
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• On General Off-Shell Representations of Worldline (1D) Supersymmetry
• Conformal mechanics
• ${\mathbb{Z}}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics
• Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes
• N=4 l-conformal Galilei superalgebra
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• Generic HKT geometries in the harmonic superspace approach
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Supersymmetric V-systems
• N=8 superconformal mechanics: direct construction
• On the spectrum-generating superalgebras of the deformed one-dimensional quantum oscillators
• The geometry of gauged (super)conformal mechanics
• Bi-HKT and bi-Kaehler supersymmetric sigma models
• Superfield approach to higher derivative N=1 superconformal mechanics
• N=2 supersymmetric extensions of relativistic Toda lattice
• Transmuted spectrum-generating algebras and detectable parastatistics of the Superconformal Quantum Mechanics
• A three-dimensional superconformal quantum mechanics with $sl(2|1)$ dynamical symmetry
• On $OSp(N|2)$ superconformal mechanics
• Spinning particles on 2-sphere in accord with the Bianchi classification
• Quantum SU$(2|1)$ supersymmetric ${\mathbb{C}}^N$ Smorodinsky--Winternitz system
• Exotic nonlinear supersymmetry and integrable systems
• Super Landau Models on Odd Cosets
• The N = 1 Supersymmetric Wong Equations and the Non-Abelian Landau Problem
• Supersymmetric Calogero models from superfield gauging
• Index and localization for type B superconformal mechanics on singular spaces
• Target duality in N=8 superconformal mechanics and the coupling of dual pairs
• Global Symmetries of Quaternion-K$\ddot{\mathbf{a}}$hler $\mathcal{N}=4$ Supersymmetric Mechanics
• Relativistic generalization of the rational Calogero model
• Weak supersymmetric $su(N|1)$ quantum systems