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The superconformal index $Z$ of the 6d (2,0) theory on $S^5 \times S^1$(which is related to the localization partition function of 5d SYM on $S^5$)should be captured at large $N$ by the quantum M2 brane theory in the dualM-theory background. Generalizing the type IIA string theory limit of thisrelation discussed in arXiv:2111.15493 and arXiv:2304.12340, we considersemiclassically quantized M2 branes in a half-supersymmetric 11d backgroundwhich is a twisted product of thermal AdS$_7$ and $S^4$. We show that theleading non-perturbative term at large $N$ is reproduced precisely by the1-loop partition function of an "instanton" M2 brane wrapped on $S^1\times S^2$with $S^2\subset S^4$. Similarly, the (2,0) theory analog of the BPS Wilsonloop expectation value is reproduced by the partition function of a "defect" M2brane wrapped on thermal AdS$_3\subset$ AdS$_7$. We comment on a curiousanalogy of these results with similar computations in arXiv:2303.15207 andarXiv:2307.14112 of the partition function of quantum M2 branes in AdS$_4\times S^7/\mathbb Z_k$ which reproduced the corresponding localizationexpressions in the ABJM 3d gauge theory.

(2,0) theory on $S^5 \times S^1$ and quantum M2 branes