New Higher-Derivative $R^4$ Theorems

TL;DR

This paper proves new theorems about the perturbative contributions to higher-derivative R^4 terms in string theory effective actions, confirming conjectures and revealing loop order constraints using the pure spinor formalism.

Contribution

It introduces two multiloop theorems relating to higher-derivative R^4 terms in superstring theory, advancing understanding of perturbative contributions and their equivalences.

Findings

For 0<n<12, no contributions above n/2 loops for ∂^n R^4 terms.

Perturbative contributions to ∂^n R^4 terms coincide for IIA and IIB when n ≤ 8.

Proves conjectures related to higher-derivative R^4 terms using pure spinor formalism.

Abstract

The non-minimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative $R^4$ conjectures of Green, Russo and Vanhove. The first theorem states that when $0<n<12$, $\partial^n R^4$ terms in the Type II effective action do not receive perturbative contributions above $n/2$ loops. The second theorem states that when $n\leq 8$, perturbative contributions to $\partial^n R^4$ terms in the IIA and IIB effective actions coincide.