Two-Loop Computation in Superstring Theory

TL;DR

This paper reviews two-loop superstring amplitude computations, discusses the vanishing of certain two-loop corrections, and introduces recent methods using hyperelliptic language and new gauge fixing techniques.

Contribution

It consolidates previous results and introduces new computational approaches for two-loop superstring amplitudes using hyperelliptic language and advanced gauge fixing.

Findings

Confirmation of the vanishing two-loop correction to the R^4 term

Review of old and new two-loop amplitude computations

Introduction of hyperelliptic language methods in superstring calculations

Abstract

In 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.