The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity

TL;DR

The paper demonstrates that the flat-space limit of the Mellin amplitude for the ABJM stress-tensor four-point function yields the momentum expansion of the 11D graviton S-matrix, enabling extraction of the $R^4$ term from CFT data. By combining the Mellin-space framework with ${ m AdS}_4/{ m CFT}_3$ holography and exact localization results for short multiplets, the authors fix the leading tree-level supergravity piece and the first nontrivial higher-derivative correction, showing exact agreement with the known $R^4$ coefficient in M-theory. The approach uses supersymmetric Ward identities to constrain the space of Mellin solutions and translates CFT data (OPE coefficients and dimensions) into flat-space scattering information via the large $c_T$ expansion. This establishes a concrete bridge from precise CFT data to the M-theory effective action, offering a pathway to bound or determine further higher-derivative terms using bootstrap methods and to extend to additional holographic SCFTs. The work highlights the potential to reconstruct the M-theory graviton S-matrix from CFT input and motivates future explorations of higher-point amplitudes and less supersymmetric settings.

Abstract

We show that by studying the flat spacetime limit of the Mellin amplitude associated with the four-point correlation function of scalar operators in the stress tensor multiplet of ABJM theory, one can produce the momentum expansion of the M-theory four-graviton S-matrix elements. Using CFT data previously obtained from the supersymmetric localization method, we carry out this procedure explicitly to the second nontrivial order in the momentum expansion, and recover precisely the known $R^4$ contribution to the scattering amplitude of super-gravitons in M-theory in eleven dimensions.