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

TL;DR

This paper studies the quantum M2 brane theory in a specific 11d background to reproduce non-perturbative effects and Wilson loop expectations in the 6d (2,0) theory on $S^5 imes S^1$, linking superconformal indices to M2 brane configurations.

Contribution

It extends the understanding of the 6d (2,0) theory's superconformal index by explicitly matching non-perturbative terms with quantum M2 brane partition functions in a twisted background.

Findings

Non-perturbative terms match 1-loop M2 brane partition functions.

Wilson loop analogs are reproduced by defect M2 branes.

Results show a deep connection between superconformal indices and quantum M2 branes.

Abstract

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 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 AdS$_7$ and $S^4$. 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 $S^1\times S^2$ with $S^2\subset S^4$. 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$_3\subset$ AdS$_7$. 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$_4 \times S^7/\mathbb Z_k$ which reproduced the corresponding localization expressions in the ABJM 3d gauge theory.