  We derive recursion relations for the anomalous dimensions of double-trace
operators occurring in the conformal block expansion of four-point stress
tensor correlators in the 6d $(2,0)$ theory, which encode higher-derivative
corrections to supergravity in $AdS_7 \times S^4$ arising from M-theory. As a
warm-up, we derive analogous recursion relations for four-point functions of
scalar operators in a toy non-supersymmetric 6d conformal field theory.
