One loop in $D=11$ vs $D=10$: 4-point check
Abstract
The one-loop correction to eleven-dimensional supergravity involves a cubically divergent term , 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.
Cite
@article{arxiv.2506.16391,
title = {One loop in $D=11$ vs $D=10$: 4-point check},
author = {Aviral Aggarwal and Subhroneel Chakrabarti and Steven Weilong Hsia and Ahmed Rakin Kamal and Linus Wulff},
journal= {arXiv preprint arXiv:2506.16391},
year = {2026}
}
Comments
13+8pp; v2: Important error in Ricci terms from string amplitudes corrected. Reduction from D=11 now matches one-loop type IIA amplitudes. v3: D=11 Lagrangian simplified, published version