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We discuss 1d and 2d global conformal field theories from the point of view of integrability, where conformal blocks are understood as eigenfunctions of Casimir differential operators with boundary conditions dictated by the operator product expansion. We uncover an interesting relationship between six-point conformal blocks in the comb channel and free-particle wavefunctions on AdS3, which we generalize for a special class of channels to higher-point conformal blocks on products of AdS3, with the remaining channels obtained through repeated uses of appropriate limits. Integrable systems associated to 1d and 2d conformal field theories may therefore be seen as limits of free theory, exhibiting a relation between AdS and CFT outside the standard AdS/CFT conjecture.