M-theory reconstruction from (2,0) CFT and the chiral algebra conjecture

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 [1] between the quantum W-N algebra and the A(N-1) (2, 0) CFT. We further explain how the 1/N expansion of 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.