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

The superconformal index Z of the 6d (2,0) theory on S5 x 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 x S2 with S2 c 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 AdS3 c 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 AdS4 x S7/DOUBLE-STRUCK CAPITAL Zk which reproduced the corresponding localization expressions in the ABJM 3d gauge theory.

Automated summary

This article investigates the superconformal index Z of the 6d (2,0) theory on S5 x S1 and describes it using the quantum M2 brane theory in the large N limit. By studying M2 branes in a twisted product of thermal AdS7 and S4, the leading non-perturbative term at large N is shown to be reproduced by the 1-loop partition function of an instanton M2 brane wrapped on S1 x S2 with S2 c S4. Similarly, the partition function of a defect M2 brane wrapped on thermal AdS3 c AdS7 reproduces the BPS Wilson loop expectation value in the (2,0) theory. The article also comments on the analogy of these results with similar computations in the quantum M2 brane partition function in AdS4 x S7/DOUBLE-STRUCK CAPITAL Zk, which reproduced the corresponding localization expressions in the ABJM 3d gauge theory.