(Super)conformal many-body quantum mechanics with extended supersymmetry

Abstract

We study N=4 supersymmetric quantum-mechanical many-body systems with M bosonic and 4M fermionic degrees of freedom. We also investigate the further restrictions of conformal and superconformal invariance. In particular, we construct conformal N=4 extensions of the A_{M-1} Calogero models, which for generic values of the coupling constant are not SU(1,1|2) superconformal. This class of models is also extended to arbitrary (even) N. We give both hamiltonian and (classical) lagrangean formulations. In the latter case we use both component and N=4 superfield formulations.

16 pages, LaTeX2e; minor corrections, references added

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Cited by in corpus (62)

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• New D(2,1;alpha) Mechanics with Spin Variables
• Calogero models and nonlocal conformal transformations
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• N=4 mechanics, WDVV equations and roots
• New insight into WDVV equation
• Many-particle mechanics with D(2,1;alpha) superconformal symmetry
• N=4 supersymmetric 3-particles Calogero model
• Superconformal mechanics and nonlinear supersymmetry
• Remark on quantum mechanics with N=2 Schrodinger supersymmetry
• D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics
• Many-Body Superconformal Systems from Hamiltonian Reductions
• Super-Calogero-Moser-Sutherland systems and free super-oscillators : a mapping
• N=4 superconformal n-particle mechanics via superspace
• Interaction via reduction and nonlinear superconformal symmetry
• $\mathcal{N}$-extended supersymmetric Calogero models
• Conformal mechanics on rotating Bertotti-Robinson spacetime
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• Comments on N=4 Superconformal Extension of the Calogero Model
• Four types of (super)conformal mechanics: D-module reps and invariant actions
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Harmonic N=2 Mechanics
• Extended superconformal symmetry and Calogero-Marchioro model
• From worldline to quantum superconformal mechanics with/without oscillatorial terms: $D(2,1;\alpha )$ and $sl(2|1)$ models
• Supersymmetric many-body Euler-Calogero-Moser model
• Super-Calogero model with OSp(2|2) supersymmetry : is the construction unique?
• New potentials for conformal mechanics
• Rational deformations of conformal mechanics
• N=4 superconformal mechanics from the su(2) perspective
• Extended supersymmetric Calogero model
• Membrane Quantum Mechanics
• N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• N=4 Multi-Particle Mechanics, WDVV Equation and Roots
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• Ruijsenaars-Schneider three-body models with N=2 supersymmetry
• $\mathcal{N}=4$ supersymmetric mechanics on curved spaces
• Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and $\mathcal{N}=4$ mechanics
• Superconformal quantum mechanics and the exterior algebra
• SU(2$|$1) supersymmetric mechanics on curved spaces
• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Harmonic Superfields in N=4 Supersymmetric Quantum Mechanics
• Superconformal SU(1,1|n) mechanics
• Comments on dihedral and supersymmetric extensions of a family of Hamiltonians on a plane
• Supersymmetric V-systems
• Super 0--brane action on the coset space of $D(2,1;\alpha )$ supergroup
• New Super Calogero Models and OSp(4|2) Superconformal Mechanics
• The curved WDVV equations and superfields
• $SU(1,1|N)$ superconformal mechanics with fermionic gauge symmetry
• Twisted Superalgebras and Cohomologies of the N=2 Superconformal Quantum Mechanics
• On $OSp(N|2)$ superconformal mechanics
• Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanics
• General realization of N=4 supersymmetric quantum mechanics and its applications
• Supersymmetric Calogero models from superfield gauging
• N=4 Mechanics, WDVV Equations and Polytopes
• Integrability of supersymmetric Calogero-Moser models