Asymptotic Factorisation of the Ground-State for SU(N)-invariant Supersymmetric Matrix-Models
Abstract
We give a simple - straightforward and rigorous - derivation that when the eigenvalues of one of the d=9 (5,3,2) matrices in the SU(N) invariant supersymmetric matrix model become large (and well separated from each other) the ground-state wavefunction (resp. asymptotic zero-energy solution of the corresponding differential equation) factorizes, for all N>1, into a product of supersymmetric harmonic oscillator wavefunctions (involving the `off-diagonal' degrees of freedom) and a wavefunction that is annihilated by the free supercharge formed out of all `diagonal' (Cartan sub-algebra) degrees of freedom.
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