Absence of $D^4 R^4$ in M-Theory From ABJM

TL;DR

This paper proves the absence of the $D^4 R^4$ interaction in M-theory by calculating 4-point supergraviton amplitudes from ABJM theory, using supersymmetric localization and Mellin amplitudes, extending previous work on $R^4$ interactions.

Contribution

It introduces a novel method to confirm the absence of the $D^4 R^4$ term in M-theory through amplitude calculations from ABJM theory, utilizing supersymmetric localization and Mellin space techniques.

Findings

Confirmed the absence of $D^4 R^4$ interaction in M-theory.

Extended previous amplitude calculations to higher derivative order.

Related 4-point functions of superconformal primaries to descendants.

Abstract

Supersymmetry allows a $D^4 R^4$ interaction in M-theory, but such an interaction is inconsistent with string theory dualities and so is known to be absent. We provide a novel proof of the absence of the $D^4 R^4$ M-theory interaction by calculating 4-point scattering amplitudes of 11d supergravitons from ABJM theory. This calculation extends a previous calculation performed to the order corresponding to the $R^4$ interaction. The new ingredient in this extension is the interpretation of the fourth derivative of the mass deformed $S^3$ partition function of ABJM theory, which can be determined using supersymmetric localization, as a constraint on the Mellin amplitude associated with the stress tensor multiplet 4-point function. As part of this computation, we relate the 4-point function of the superconformal primary of the stress tensor multiplet of any 3d ${\cal N} = 8$ SCFT to some of the 4-point functions of its superconformal descendants. We also provide a concise formula for a general integrated 4-point function on $S^d$ for any $d$.