## Abstract

We present a quantum M2 brane computation of the instanton prefactor in the leading non-perturbative contribution to the ABJM 3-sphere free energy at large N and fixed level k. Using supersymmetric localization, such instanton contribution was found earlier to take the form Finst(Nk)=−(sin22πk)−1exp(−2π2Nk)+.… The exponent comes from the action of an M2 brane instanton wrapped on S ^{3}/ℤ_{ k}, which represents the M-theory uplift of the ℂP^{1} instanton in type IIA string theory on AdS_{4} × ℂP^{3}. The IIA string computation of the leading large k term in the instanton prefactor was recently performed in arXiv:2304.12340. Here we find that the exact value of the prefactor (sin22πk)−1 is reproduced by the 1-loop term in the M2 brane partition function expanded near the S ^{3}/ℤ_{ k} instanton configuration. As in the Wilson loop example in arXiv:2303.15207, the quantum M2 brane computation is well defined and produces a finite result in exact agreement with localization.

Original language | English (US) |
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Article number | 29 |

Journal | Journal of High Energy Physics |

Volume | 2023 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2023 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Keywords

- AdS-CFT Correspondence
- M-Theory
- P-Branes