  We determine in a closed form all scalar one-point functions of the defect
CFT dual to the D3-D5 probe brane system with k units of flux which amounts to
calculating the overlap between a Bethe eigenstate of the integrable SO(6) spin
chain and a certain matrix product state of bond dimension k. In particular, we
show that the matrix product state is annihilated by all the parity odd charges
of the spin chain which has recently been suggested as the criterion for such a
state to correspond to an integrable initial state. Finally, we discuss the
properties of the analogous matrix product state for the SO(5) symmetric D3-D7
probe brane set-up.
