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N=8 superconformal mechanics: direct construction
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abstract
In the present paper we constructed the supercharges and Hamiltonians for all variants of superconformal mechanics associated with the superalgebras $osp(8|2), {\mathfrak F(4)}, osp(4^\star |4)$, and $su(1,1|4)$. The fermionic and bosonic fields involved were arranged into generators spanning $so(8), so(7), so(5)\oplus su(2)$ and $su(4) \oplus u(1)$ $R$-symmetry currents of the corresponding superconformal algebras. The bosonic and fermionic parts of these $R$-symmetry generators separately define the constants of motion and form the same algebras. The angular part of the supercharges defining the system have the structure ``$(R-symmetry\; generators)\, \times\, fermions$'' while the angular part of Hamiltonian is just a proper sum of full Casimir operators and its purely bosonic and fermionic parts. We also constructed the explicit embedding of the algebras $so(7), \, so(5) \times su(2)$, and $su(4)\times u(1)$ into $so(8)$, which provide the possibility to explicitly construct the corresponding supercharges.
Forward citations
Cited by 4 Pith papers
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${\cal N}{=}\,4$ supersymmetric multiparticle systems based on indecomposable multiplets
Nonlinear indecomposable multiplets (1,4,3)⊃+(4,4,0) produce new N=4 supersymmetric deformations of U(2)-spin rational Calogero models invariant under OSp(4|2), plus a near-equivalent hyperbolic version.
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Superconformal mechanics from N-extended Euler-Calogero-Moser and Calogero models
Center-of-mass decoupling of two-particle N-extended ECM and Calogero models yields SU(1,1|N) or Osp(N|2) superconformal mechanics that admit bosonic spin variables.
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${\cal N}{=}\,4$ supersymmetric multiparticle systems based on indecomposable multiplets
New N=4 supersymmetric generalizations of U(2)-spin rational and hyperbolic Calogero systems are constructed using nonlinear indecomposable supermultiplets (1,4,3)⊃+(4,4,0).
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Superconformal mechanics from N-extended Euler-Calogero-Moser and Calogero models
Two-particle N-extended Euler-Calogero-Moser models produce SU(1,1|N) superconformal mechanics after center-of-mass decoupling; the Calogero case yields only Osp(N|2).
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