Factorization of a two-loop four-point superstring amplitude.

Abstract

The behavior of the two-loop four-point graviton amplitude is investigated in the type-II superstring theory, where the genus-two Riemann surface degenerates into two tori. The amplitude turns out to be finite in this limit and it is shown explicitly to the lowest order of the pinching parameter that it produces the product of two one-loop amplitudes, as is expected from the factorization property.