In this talk, based on the work to appear, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function, and its generalization to the primary operator exchange with continuous spin which is relevant for Lorentzian spacetime. Using these results we apply the Lorentzian inversion formula to compute so-called crossing kernel in general spacetime dimensions, and the result can be written as a double infinite summation over certain Kempe de Feriet hypergeometric functions. During the talk, we will introduce various physical quantities and discuss their subtitles and applications.

I will begin with basic review on the integrabilities in AdS/CFT correspondence, and move on discussing the role of scattering matrices in gauge and string thoeries. I will then explain the formation of magnon boundststates in gauge theory and their corresponding classical string solution. The scattering of magnon boundstates and their classifications will also be discussed in this seminar. I will also mention some work in progress.