N=8 superconformal mechanics: direct construction

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.