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It was shown in arXiv:2309.10786 that the leading non-perturbative contribution to the large N expansion of the superconformal index of the (2,0) 6d theory (which describes low-energy dynamics of N coincident M5 branes) is reproduced by the semiclassical partition function of quantum M2 brane wrapped on S1×S2 in a twisted version of AdS×7S4 background. Here we demonstrate an analogous relation for the leading non-perturbative contribution to the large N expansion of the superconformal index of the N=8 supersymmetric level-one U(N)×U(N) ABJM theory (which describes low-energy dynamics of N coincident M2 branes). The roles of M2 and M5 branes get effectively interchanged. Namely, the large N correction to the ABJM index is found to be given by the semiclassical partition function of quantum M5 brane wrapped on S1×S5 in a twisted version of AdS×4S7 background. This effectively confirms the suggestion for the "M5 brane index" made in arXiv:2007.05213 on the basis of indirect superconformal algebra considerations.
Beccaria et al. (Fri,) studied this question.