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

Abstract

The N-point amplitudes for the Type II and Heterotic superstrings at two-loop order and for N ≤ 4 massless NS bosons are evaluated explicitly from first principles, using the method of projection onto super period 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 N ≤ 3, no two-loop corrections occur, while for N = 4, no two-loop corrections to the low energy effective action occur for R 4 terms in the Type II superstrings, and for F 4 , F 2 F 2 , F 2 R 2 , and R 4 terms in the Heterotic strings.

Superstring Scattering Amplitudes in Higher Genus

“…This was verified for the genus 2 measure in [14,15], and checking this for the proposed ansätze in genera 3 and 4 would be a good indication of their potential validity.…”

Manifesting enhanced cancellations in supergravity: integrands versus integrals

“…In this case no known standard-symmetry argument invalidates [11,12,14,47] the potential R 4 divergence. However, both field theory [10] and string theory [48] calculations show that there are no R 4 terms in the effective action.…”

The Vanishing of Two-Point Functions for Three-Loop Superstring Scattering Amplitudes

“…Our proof uses the reformulation of ansatz given in [8], theta functions, and specifically the theory of the Γ 00 linear system on Jacobians introduced by van Geemen and van der Geer [6]. At the two-loop level, where the amplitudes were computed by D'Hoker and Phong [11,12,13,14,17,18], we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera [8,24,3].…”