A simplifying feature of the heterotic one loop four graviton amplitude

TL;DR

This paper demonstrates that certain weight four modular graph functions in heterotic string theory's one-loop four graviton amplitude are inherently simple and do not require regularization, unlike other similar terms.

Contribution

It reveals a simplifying property of specific modular graph functions in heterotic string theory, showing their integrands are regularization-free and establishing relations between different graph topologies.

Findings

Weight four modular graph functions are regularization-free.

Relations between different graph topologies are established.

The property persists for infinitely many terms in the effective action.

Abstract

We show that the weight four modular graph functions that contribute to the integrand of the t_8 t_8 D^4 R^4 term at one loop in heterotic string theory do not require regularization, and hence the integrand is simple. This is unlike the graphs that contribute to the integrands of the other gravitational terms at this order in the low momentum expansion, and these integrands require regularization. This property persists for an infinite number of terms in the effective action, and their integrands do not require regularization. We find non--trivial relations between weight four graphs of distinct topologies that do not require regularization by performing trivial manipulations using auxiliary diagrams.