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We study existence and uniqueness of solution for stochastic differentialequations with distributional drift by giving a meaning to the Stroock-Varadhanmartingale problem associated such equations. The approach we exploit is theone of paracontrolled distributions introduced in [13]. As a result we makesense of the three dimensional polymer measure with white noise potential.

Multidimensional SDEs with singular drift and universal construction of the polymer measure with white noise potential