N=8 superconformal mechanics: direct construction

TL;DR

This paper explicitly constructs supercharges and Hamiltonians for various superconformal mechanics models associated with specific superalgebras, detailing their algebraic structure and embeddings.

Contribution

It provides a direct construction of supercharges and Hamiltonians for superconformal mechanics related to multiple superalgebras, including explicit algebra embeddings.

Findings

Constructed supercharges and Hamiltonians for all variants of superconformal mechanics studied.

Detailed the algebraic structure of R-symmetry generators and their role in the dynamics.

Provided explicit embeddings of certain algebras into so(8).

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.