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The dynamics of heavy quarkonium systems in the strong coupling regimereduces to a quantum mechanical problem with a number of potentials which maybe organized in powers of 1/m, m being the heavy quark mass. The potentialsmust be calculated non-perturbatively, for instance in lattice QCD. It is wellknown that the long distance behavior of the static (1/m^0) potential is wellreproduced by an effective string theory. We show that this effective stringtheory, if correct, should also reproduce the long distance behavior of all 1/msuppressed potentials. We demonstrate the practical usefulness of this resultby finding a suitable parameterization of the recently calculated 1/mpotential. We also calculate the 1/m^2 velocity dependent and spin dependentpotentials. Once Poincar\'e invariance is implemented, the shapes of most ofthe spin independent potentials are fully predicted in terms of the stringtension, and the shapes of the spin dependent ones in terms of a singleparameter.

Effective string theory constraints on the long distance behavior of the subleading potentials