Finite-N corrections to the M-brane indices

A bstract We investigate finite- N corrections to the superconformal indices of the theories realized on M2- and M5-branes. For three-dimensional theories realized on a stack of N M2-branes we calculate the finite- N corrections as the contribution of extended M5-branes in the dual geometry AdS 4 × S 7 . We take only M5-brane configurations with a single wrapping into account, and neglect multiple-wrapping configurations. We compare the results with the indices calculated from the ABJM theory, and find agreement up to expected errors due to the multiple wrapping. For six-dimensional theories on N M5-branes we calculate the indices by analyzing extended M2-branes in AdS 7 × S 4 . Again, we include only configurations with single wrapping. We first compare the result for N = 1 with the index of the free tensor multiplet to estimate the order of the error due to multiple wrapping. We calculate first few terms of the index of A N − 1 theories explicitly, and confirm that they can be expanded by superconformal representations. We also discuss multiple-wrapping contributions to the six-dimensional Schur-like index.