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We derive the planar large N non-supersymmetric background of the quantummechanical hamiltonian of two hermitean matrices coupled via a Yang-Millsinteraction, in terms of the density of eigenvalues of one of the matrices.This background satisfies an implicit non linear integral equation, with aperturbative small coupling expansion and a solvable large coupling solution,which is obtained. The energy of system and the expectation value of severalcorrelators are obtained in this strong coupling limit. They are free ofinfrared divergences.

Non supersymmetric strong coupling background from the large N quantum mechanics of two matrices coupled via a Yang-Mills interaction