Abstract
We study various aspects of the M-theory uplift of the AN −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 R4 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 {mathcal{W}}_N algebra and the AN −1 (2, 0) CFT. We further explain how the 1/N expansion of {mathcal{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.
Highlights
Flat space, whose gravitational backreaction generates an AdS7 × S4 solution of M-theory
We show how knowledge of operator product expansion (OPE) coefficients and scaling dimensions for this CFT can be directly translated into features of the momentum expansion of M-theory
An initial implementation of the numerical bootstrap to the (2,0) CFT was performed in [10], which led to the first predictions for finite N data for low-lying non-BPS operators that appear in the stress tensor operator product expansion (OPE)
Summary
Conformal symmetry and so(5) symmetry implies that the four point function of Sk(x, Y ) takes the form. The uplift to 6d implies that all half-BPS OPE coefficients not involving S2, the stress-tensor multiplet, have 1/c expansions of the form (1.5). This is precisely the structure one expects based on the cubic coupling φ1φ2φ3 in the quantum effective action in AdS7. The form of (2.23) follows from dimensional analysis, (LAdS/ 11)9 ∝ c, combined with the fact that the reduction on M can only produce powers of LAdS, not 11.11 To relate g123 to the dual CFT OPE coefficient λk1k2k3, one multiplies (2.23) by a function with an infinite expansion in non-negative integer powers of 1/c ∼ GN , which accounts for bulk loops. M-theory, in particular, the absence of 10- and 12-derivative terms
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