One loop in $D=11$ vs $D=10$: 4-point check

TL;DR

This paper verifies the consistency of one-loop corrections involving Riemann tensors and RR fields in M-theory and type IIA string theory, extending previous results to include NSNS and RR couplings using pure spinor formalism.

Contribution

It extends the verification of one-loop couplings in M-theory to include NSNS and RR fields, correcting previous literature and providing a simplified form of 4-point terms in eleven dimensions.

Findings

Confirmed agreement of couplings involving RR fields and dilaton.

Extended previous 4-point results to NSNS and RR sectors.

Provided a simplified expression for 4-point terms in eleven dimensions.

Abstract

The one-loop correction to eleven-dimensional supergravity involves a cubically divergent term $t_8t_8R^4$, with four Riemann tensors. A similar term (with finite coefficient) has been argued to be present in the M-theory effective action. It is expected to reduce to a similar one-loop term present in the type IIA effective action. This has previously been verified in the NSNS sector at the 4-point level. Here we extend this result to couplings of NSNS and RR fields, which have been computed using the pure spinor formalism. In particular, we check all couplings of RR fields to the dilaton as well as all couplings involving the metric and RR three-form. Correcting some minor mistakes in the literature we find complete agreement. We also give a complete analysis of 4-point terms in eleven dimensions computed previously from superparticle amplitudes and present a very simple form for these.