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

DOI10.1007/JHEP08(2018)116zbMATH Open1396.81170arXiv1805.00892WikidataQ122966875 ScholiaQ122966875MaRDI QIDQ1783846

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Publication date: 21 September 2018

Published in: (Search for Journal in Brave)

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 ${calW}_N$ algebra and the $A_{N-1}$ $(2,0)$ CFT. We further explain how the $1/N$ expansion of ${calW}_N$ structure constants exhibits the structure of protected vertices in the M-theory action. Conversely, our results provide strong evidence for the chiral algebra conjecture.

Full work available at URL: https://arxiv.org/abs/1805.00892

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