Comments on Two-Loop Four-Particle Amplitude in Superstring Theory

TL;DR

This paper demonstrates the equivalence of two-loop four-particle amplitudes in superstring theory with previous results, emphasizing the role of ${f Z}_2$ symmetry in hyperelliptic Riemann surfaces for the proof.

Contribution

It provides a proof of the equivalence of different two-loop four-particle amplitude calculations in superstring theory using hyperelliptic Riemann surface symmetry.

Findings

Two-loop four-particle amplitudes are equivalent across different methods.

${f Z}_2$ symmetry is crucial in establishing this equivalence.

The proof consolidates previous results in superstring amplitude calculations.

Abstract

It is shown that the four-particle amplitude of superstring theory at two loops obtained in [1,2] is equivalent to the previously obtained results in [3,4,5]. Here the ${\bf Z}_2$ symmetry in hyperelliptic Riemann surface plays an important role in the proof.