  We study form factors in the light-cone gauge world-sheet theory for strings
in AdS_5 x S^5. We perturbatively calculate the two-particle form factor in a
closed su(2) sector to one-loop in the near-plane-wave limit and to two-loops
in the Maldacena-Swanson limit. We also perturbatively solve the functional
equation which follows from the form factor axioms for the world-sheet theory
and show that the "minimal" solution correctly reproduces the discontinuities
of the perturbative calculations. Finally we propose a prescription, valid for
polynomial orders of the inverse world-sheet length, for extracting the
finite-volume world-sheet matrix element from the form factors and show that
the two-excitation matrix element matches with the thermodynamic limit of the
spin-chain description of certain tree-level N=4 SYM structure constants.
