The D^{10} R^4 term in type IIB string theory

TL;DR

This paper derives the differential equation governing the D^{10} R^4 term in type IIB string theory's effective action, predicting vanishing perturbative contributions beyond three loops and providing loop coefficient estimates.

Contribution

It determines the Poisson equation for the D^{10} R^4 term using known scattering data, advancing understanding of higher derivative corrections in string theory.

Findings

Perturbative contributions vanish above three loops.

Provides predictions for two and three loop coefficients.

Establishes the differential equation for the D^{10} R^4 term.

Abstract

The modular invariant coefficient of the D^{2k} {\cal{R}}^4 term in the effective action of type IIB superstring theory is expected to satisfy Poisson equation on the fundamental domain of SL(2,Z). Under certain assumptions, we obtain the equation satisfied by D^{10} {\cal{R}}^4 using the tree level and one loop results for four graviton scattering in type II string theory. This leads to the conclusion that the perturbative contributions to D^{10} {\cal{R}}^4 vanish above three loops, and also predicts the coefficients at two and three loops.