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arXiv · 2007.05213

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

Reona Arai·Shota Fujiwara·Yosuke Imamura·Tatsuya Mori·Daisuke Yokoyama
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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.

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Reona Arai, Shota Fujiwara, Yosuke Imamura, Tatsuya Mori, Daisuke Yokoyama. 2020-07-10. Finite-$N$ corrections to the M-brane indices. https://doi.org/10.1007/jhep11(2020)093

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