  We study the structure constant of a single trace operator and two
determinant operators in ${\cal N}=4$ super Yang-Mills theory. Holographically
such a quantity corresponds to the interaction vertex between a closed string
and two open strings attached to the spherical $D$-branes. Relying on
diagrammatic intuition, we conjecture that the structure constant at the finite
coupling is nicely written by the hexagon form factors. Precisely we need to
prepare two hexagon twist operators and appropriately glue edges together by
integrating mirror particles contributions and by contracting boundary states.
The gluing generates the worldsheet for a closed string and two open strings
attached to the $D$-branes. At the weak coupling, the asymptotic expression
simply reduces to sum over all possible partitions not only for the edge
related to the closed string but also for the edges representing the half of
the open string together with reflection effects for the opposite open string
edges. We test the conjecture by directly computing various tree level
structure constants. The result is nicely matched with our conjecture.
