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We investigate bosonic atoms or molecules interacting via dipolarinteractions in a planar array of one-dimensional tubes. We consider thesituation in which the dipoles are oriented perpendicular to the tubes by anexternal field. We find various quantum phases reaching from a `slidingLuttinger liquid' phase in which the tubes remain Luttinger liquids to atwo-dimensional charge density wave ordered phase. Two different kinds ofcharge density wave order occur: a stripe phase in which the bosons indifferent tubes are aligned and a checkerboard phase. We further point out howto distinguish the occurring phases experimentally.

Dipolar bosons in a planar array of one-dimensional tubes