Depinning transition of a directed polymer by a periodic potential: A d-dimensional solution

We study the depinning phase transition of a directed polymer in a d-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the polymer. We show that a bound state can still arise even if, in average, the potential layer is not attractive and for diverging values of the potential on the repulsive sites. Our solution can be useful in the context of kinetic growth of interfaces.