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

TL;DR

This paper computes finite-N corrections to superconformal indices of M2- and M5-brane theories by analyzing single-wrapping extended branes in dual geometries, comparing results with known theories, and discussing multiple-wrapping effects.

Contribution

It provides explicit calculations of finite-N corrections to superconformal indices for M-brane theories using dual geometry configurations, focusing on single-wrapping contributions.

Findings

Finite-N corrections match ABJM indices within expected errors.

Explicit index calculations for N=1 M5-branes agree with free tensor multiplet.

Superconformal representation expansion confirmed for A_{N-1} theories.

Abstract

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 $AdS_4\times \boldsymbol{S}^7$. 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 $AdS_7\times \boldsymbol{S}^4$. 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.