Simplifying the one loop five graviton amplitude in type IIB string theory

TL;DR

This paper simplifies the one-loop five graviton amplitude in type IIB string theory by expressing complex derivative-involving graphs in terms of simpler graphs without derivatives, reducing computational complexity.

Contribution

It introduces a method to rewrite derivative-containing modular graphs in terms of non-derivative graphs, simplifying the amplitude calculation.

Findings

Derivative graphs can be expressed in terms of non-derivative graphs.

Significant simplification of the five graviton amplitude at one loop.

Enhanced understanding of modular graph functions in string theory.

Abstract

We consider the D^8 R^5 and D^{10} R^5 terms in the low momentum expansion of the five graviton amplitude in type IIB string theory at one loop. They involve integrals of various modular graph functions over the fundamental domain of SL(2,Z). Unlike the graphs which arise in the four graviton amplitude or at lower orders in the momentum expansion of the five graviton amplitude where the links are given by scalar Green functions, there are several graphs for the D^8 R^5 and D^{10} R^5 terms where two of the links are each given by a derivative of the Green function. Starting with appropriate auxiliary diagrams, we show that these graphs can be expressed in terms of those which do not involve any derivatives. This results in considerable simplification of the amplitude.