(2,0) theory on S5 × S1 and quantum M2 branes

The superconformal index Z of the 6d (2,0) theory on S5×S1 (which is related to the localization partition function of 5d SYM on S5) should be captured at large N by the quantum M2 brane theory in the dual M-theory background. Generalizing the type IIA string theory limit of this relation discussed in arXiv:2111.15493 and arXiv:2304.12340, we consider semiclassically quantized M2 branes in a half-supersymmetric 11d background which is a twisted product of thermal AdS7 and S4. We show that the leading non-perturbative term at large N is reproduced precisely by the 1-loop partition function of an “instanton” M2 brane wrapped on S1×S2 with S2⊂S4. Similarly, the (2,0) theory analog of the BPS Wilson loop expectation value is reproduced by the partition function of a “defect” M2 brane wrapped on thermal AdS⊂3 AdS7. We comment on a curious analogy of these results with similar computations in arXiv:2303.15207 and arXiv:2307.14112 of the partition function of quantum M2 branes in AdS×4S7/Zk which reproduced the corresponding localization expressions in the ABJM 3d gauge theory.