Two-loop superstrings VI Nonrenormalization theorems and the 4-point function Original Research Article

The N-point amplitudes for the type II and heterotic superstrings at two-loop order and for image massless NS bosons are evaluated explicitly from first principles, using the method of projection onto superperiod matrices introduced and developed in the first five papers of this series. The gauge-dependent corrections to the vertex operators, identified in paper V, are carefully taken into account, and the crucial counterterms which are Dolbeault exact in one insertion point and de Rham closed in the remaining points are constructed explicitly. This procedure maintains gauge slice independence at every stage of the evaluation. Analysis of the resulting amplitudes demonstrates, from first principles, that for image, no two-loop corrections occur, while for image, no two-loop corrections to the low energy effective action occur for image terms in the type II superstrings, and for image, image, image, and image terms in the heterotic strings.