M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture

TL;DR

The paper develops a concrete program to reconstruct M-theory from the 6d $A_{N-1}$ $(2,0)$ CFT by leveraging Mellin amplitudes and the ${\cal W}_N$ chiral algebra. It shows how protected and unprotected OPE data fix the momentum expansion of the 11d S-matrix, reproducing the $R^4$ term and constraining higher-derivative vertices via a flat-space limit and dimensional reduction. The main result is the exact derivation of the $R^4$ coefficient from the ${\cal W}_N$-controlled correlator $\langle S_3S_3S_3S_3\rangle$ and a detailed program to access higher derivatives from $\langle S_2S_2S_2S_2\rangle$, anchored by a precise $ frac{1}{c}$ expansion. This provides strong evidence for the Beem–Chester–Cordova chiral algebra conjecture and offers a holographic bootstrap pathway to finite-$N$ M-theory data with potential extensions to other AdS$_{d+1}\times \mathcal{M}$ setups.

Abstract

We study various aspects of the M-theory uplift of the $A_{N-1}$ series of $(2,0)$ CFTs in 6d, which describe the worldvolume theory of $N$ M5 branes in flat space. We show how knowledge of OPE coefficients and scaling dimensions for this CFT can be directly translated into features of the momentum expansion of M-theory. In particular, we develop the expansion of the four-graviton S-matrix in M-theory via the flat space limit of four-point Mellin amplitudes. This includes correctly reproducing the known contribution of the $R^4$ term from 6d CFT data. Central to the calculation are the OPE coefficients for half-BPS operators not in the stress tensor multiplet, which we obtain for finite $N$ via the previously conjectured relation [arXiv:1404.1079] between the quantum ${\cal W}_N$ algebra and the $A_{N-1}$ $(2,0)$ CFT. We further explain how the $1/N$ expansion of ${\cal W}_N$ structure constants exhibits the structure of protected vertices in the M-theory action. Conversely, our results provide strong evidence for the chiral algebra conjecture.