Worldsheet form factors in AdS/CFT

Abstract

We formulate a set of consistency conditions appropriate to worldsheet form factors in the massive, integrable but nonrelativistic, light-cone gauge fixed ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ string theory. We then perturbatively verify that these conditions hold, at tree level in the near-plane-wave limit and to one loop in the near-flat (Maldacena-Swanson) limit, for a number of specific cases. We further study the form factors in the weakly coupled dual description, verifying that the relevant conditions naturally hold for the one-loop Heisenberg spin chain. Finally, we note that the near-plane-wave expressions for the form factors, when further expanded in small momentum or, equivalently, large charge density, reproduce the thermodynamic limit of the spin-chain results at leading order.