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We investigate finite-$N$ corrections to the superconformal indices of thetheories realized on M2- and M5-branes. For three-dimensional theories realizedon a stack of $N$ M2-branes we calculate the finite-$N$ corrections as thecontribution of extended M5-branes in the dual geometry $AdS_4\times\boldsymbol{S}^7$. We take only M5-brane configurations with a single wrappinginto account, and neglect multiple-wrapping configurations. We compare theresults with the indices calculated from the ABJM theory, and find agreement upto expected errors due to the multiple wrapping. For six-dimensional theorieson $N$ M5-branes we calculate the indices by analyzing extended M2-branes in$AdS_7\times \boldsymbol{S}^4$. Again, we include only configurations withsingle wrapping. We first compare the result for $N=1$ with the index of thefree tensor multiplet to estimate the order of the error due to multiplewrapping. We calculate first few terms of the index of $A_{N-1}$ theoriesexplicitly, and confirm that they can be expanded by superconformalrepresentations. We also discuss multiple-wrapping contributions to thesix-dimensional Schur-like index.

Finite-$N$ corrections to the M-brane indices