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

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 $Ad{S}_4\times {\mathbf{S}}^7$. 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 $Ad{S}_7\times {\mathbf{S}}^4$. 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.

arXiv comment40 pages; v2: minor corrections

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• M2-branes and plane partitions
• M2-M5 giant graviton expansions
• Asymptotic degeneracies of M2-brane SCFTs
• ADHM Wilson line defect indices
• Abelian dualities and line defect indices for 3d gauge theories
• Localization and wall-crossing of giant graviton expansions in AdS${}_5$
• Giant Gravitons and Volume Minimisation