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We determine in a closed form all scalar one-point functions of the defectCFT dual to the D3-D5 probe brane system with k units of flux which amounts tocalculating the overlap between a Bethe eigenstate of the integrable SO(6) spinchain and a certain matrix product state of bond dimension k. In particular, weshow that the matrix product state is annihilated by all the parity odd chargesof the spin chain which has recently been suggested as the criterion for such astate to correspond to an integrable initial state. Finally, we discuss theproperties of the analogous matrix product state for the SO(5) symmetric D3-D7probe brane set-up.

Scalar one-point functions and matrix product states of AdS/dCFT