M-theory Beyond The Supergravity Approximation

TL;DR

This work uses the conformal bootstrap and crossing symmetry to probe M-theory beyond the supergravity limit in AdS$_7\times S^4$ by studying the four-point function of stress-tensor multiplets in the 6d $(2,0)$ theory. Solving the crossing equations in a large-$N$ expansion with spin truncated to 0, 2, and 4 reveals a leading spin-0 correction scaling as $N^{-5}$, interpreted as an M-theoretic analogue of $\mathcal{R}^4$ in 11d supergravity; higher-spin truncations are more suppressed, by at least $N^{-19/3}$, and thus subleading to the anticipated 1-loop supergravity term. The results provide a concrete bootstrap-based handle on the low-energy effective action of M-theory on $AdS_7\times S^4$ and suggest concrete directions to extract further quantum corrections, including the yet-to-be-computed 1-loop contribution. The approach echoes analogous analyses in $\mathcal{N}=4$ SYM and spatially extends the bootstrap program to the 6d $(2,0)$ theory, offering a pathway to derive correlation functions and effective actions from first principles.

Abstract

We analyze the four-point function of stress-tensor multiplets for the 6d quantum field theory with $OSp(8^*|4)$ symmetry which is conjectured to be dual to M-theory on $AdS_7 \times S^4$, and deduce the leading correction to the tree-level supergravity prediction by obtaining a solution of the crossing equations in the large-$N$ limit with the superconformal partial wave expansion truncated to operators with zero spin. This correction corresponds to the M-theoretic analogue of $\mathcal{R}^4$ corrections in string theory. We also find solutions corresponding to higher-spin truncations, but they are subleading compared to the 1-loop supergravity prediction, which has yet to be calculated.