Dynamical symmetries in supersymmetric matrix models (Q930097)

In a supersymmetric matrix model with supersymmetric hamiltonian \(H\), the authors study its asymptotic part \(H^\infty\). Firstly, they showed that it decomposes (like the hamiltonian \(H\)) in a bosonic part \(H_B^\infty\) and a fermionic part \(H_F^\infty\). The bosonic part is a sum of harmonic oscillators with ground state \(s = 2(d-1)\), which leads the authors to study the spectral properties of \(s + H_F^\infty\). In the particular case where the dimension \(d=9\), they showed that \(s + H_F^\infty\) reveals a dynamical \(SU(2)\) symmetry. For the zero energy of the fermionic part, they showed that the equation for the ground state can be transformed in a system of equation which can be solved, under certain conditions, by a recursive procedure. Finally, they also point out some additional properties of the model.