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

Damon J. Binder; Shai M. Chester; Silviu S. Pufu

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arXiv · 1808.10554

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

Damon J. Binder·Shai M. Chester·Silviu S. Pufu

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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 $d$.

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Damon J. Binder, Shai M. Chester, Silviu S. Pufu. 2018-08-31. Absence of $D^4 R^4$ in M-Theory From ABJM. https://arxiv.org/abs/1808.10554

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