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It was shown in arXiv:2309.10786 that the leading non-perturbativecontribution to the large $N$ expansion of superconformal index of (2,0) 6dtheory (which describes low-energy dynamics of $N$ coincident M5 branes) isreproduced by the semiclassical partition function of quantum M2 brane wrappedon $S^{1}\times S^{2}$ in a twisted version of AdS$_{7}\times S^{4}$background. Here we demonstrate an analogous relation for the leadingnon-perturbative contribution to the large $N$ expansion of the superconformalindex of the ${n}=8$ supersymmetric level-one $U(N) \times U(N)$ ABJM theory(which describes low-energy dynamics of $N$ coincident M2 branes). The roles ofM2 and M5 branes get effectively interchanged. Namely, the large $N$ correctionto the ABJM index is found to be given by the semiclassical partition functionof quantum M5 brane wrapped on $S^1 \times S^5$ in a twisted version ofAdS$_{4}\times S^{7}$ background. This effectively confirms the suggestion forthe "M5 brane index" made in arXiv:2007.05213 on the basis of indirectsuperconformal algebra considerations.

Large N expansion of superconformal index of k=1 ABJM theory and semiclassical M5 brane partition function