Two-Loop Superstrings in Hyperelliptic Language II: the Vanishing of the Cosmological Constant and the Non-Renormalization Theorem

TL;DR

This paper verifies the vanishing of the cosmological constant and the non-renormalization theorem at two loops in superstring theory using hyperelliptic language and a new chiral measure, simplifying amplitude calculations.

Contribution

It introduces a set of identities that simplify two-loop superstring amplitude calculations and confirms key theoretical properties using explicit computation.

Findings

Confirmed vanishing of the cosmological constant at two loops

Validated the non-renormalization theorem at two loops

Simplified four-particle amplitude calculations

Abstract

The vanishing of the cosmological constant and the non-renormali-zation theorem are verified at two loops by explicit computation using the hyperelliptic language and the newly obtained chiral measure of D'Hoker and Phong. A set of identities is found which is used in the verification of the non-renormalization theorem and leads to a great simplification of the calculation of the four-particle amplitude at two loops.