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 $osp\left(8\right|2),F(4),osp(4^{\star }\left|4\right)$, and $su(1,1|4)$. The fermionic and bosonic fields involved were arranged into generators spanning $so\left(8\right),so\left(7\right),so\left(5\right)\oplus su\left(2\right)$ and $su\left(4\right)\oplus u\left(1\right)$ 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 “$(R-symmetrygenerators)\times fermions$” 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 $so\left(7\right),so\left(5\right)\times su\left(2\right)$, and $su\left(4\right)\times u\left(1\right)$ into $so\left(8\right)$, which provide the possibility to explicitly construct the corresponding supercharges.