2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51737In this paper I review some old and new works on the computation of two-loop 4-particle amplitude in superstring theory. I also present the proof by Iengo, showing the vanishing of the term related to the two-loop correction to the $R^4$ term. Finally I will present some recent works on two-loop computation in hyperelliptic language following the new gauging fixing method of D'Hoker and Phong.LaTex file, 30 pagesHigh Energy Physics - Theorytext