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

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 x S2 in a twisted version of AdS7 x S4 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) x 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 x S5 in a twisted version of AdS4 x S7 background. This effectively confirms the suggestion for the "M5 brane index" made in arXiv :2007 .05213 on the basis of indirect superconformal algebra considerations.