Abstract
We present a model of SU( N) lattice Yang-Mills theory which exhibits asymptotic freedom and permanent quark confinement simultaneously. We argue that in the limit of vanishing bare gauge-coupling constant, the model is approximately mapped by a duality transformation to the confining phase of a Z( N) lattice gauge model. Existence of the continuum limit with the vanishingly small bare coupling constant (asymptotic freedom) requires us to make the duality map at the critical point of the Z( N) model. The mechanism of quark confinement is the condensation of magnetic monopoles and associated vortex strings which are topologically characterized by Z( N) group structure.
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