Two-loop superstrings in hyperelliptic language II: the cosmological constant and the non-renormalization theorem

The vanishing of the cosmological constant and the non-renormalization 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