From amplitudes to form factors in the $\mathcal{N}=4$ SYM theory

We discuss the latest progress in understanding the infrared behavior of inclusive cross sections and the form factors for the so-called half-BPS operators in the $\mathcal{N}=4$ SYM theory. In both cases, we observe the exponentiation of the infrared divergences while the finite parts do not have such a simple behavior. We show how the infrared divergences cancel in inclusive cross sections when the emission of soft and collinear quanta is taken into account. We calculate the finite parts of the form factors in the two-loop approximation. They are rather complicated and are expressed in terms of generalized polylogarithms of several variables. But the principle of maximal transcendentality is nevertheless still satisfied.