Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry

We present a new multiparticle model of $\mathcal{N}=8$ mechanics with superconformal $F(4)$ symmetry. The system is constructed in terms of two matrix $\mathcal{N}=4$ multiplets. One of them is a bosonic matrix $({\bf 1, 4, 3})$multipletandanotherisafermionic$({\bf 0, 4, 4})$ one. Off-diagonal bosonic components of the $(\mathbf{1},\mathbf{4},\mathbf{3})$ multiplet are chosen to take values in the flag manifold $\mathrm{U}(n)\mathrm{/}[\mathrm{U}(1){]}^n$ and they carry additional gauge symmetries. The explicit form of the $F(4)$ supersymmetry generators is found. We demonstrate that the $F(4)$ superalgebra constructed contains as subalgebras two different $D(2,1;\alpha =-1\mathrm{/}3)$ superalgebras intersecting over the common $sl(2,\mathbb{R})\oplus su(2)$ subalgebra.