A study of integrable form factors in massless relativistic $AdS_2$

In this paper we initiate the study of form factors for the massless scattering of integrable $AdS_2$ superstrings, where the difference-form of the $S$-matrix can be exploited to implement the relativistic form factor bootstrap. The non-standard nature of the $S$-matrix implies that traditional methods do not apply. We use the fact that the massless $AdS_2$ $S$-matrix is a limit of a better-behaved $S$-matrix found by Fendley. We show that the previously conjectured massless $AdS_2$ dressing factor coincides with the limit of the De Martino - Moriconi improved dressing factor for the Fendley $S$-matrix. After finding a method to construct integral representations of relativistic dressing factors satisfying specific assumptions, we obtain analytic proofs of crossing and unitarity relations and propose a solution to the form factors constraints in the two-particle case.