Instanton contributions to the ABJM free energy from quantum M2 branes

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 The exponent comes from the action of an M2 brane instanton wrapped on S3/ℤk, which represents the M-theory uplift of the ℂP1 instanton in type IIA string theory on AdS4 × ℂP3. 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 is reproduced by the 1-loop term in the M2 brane partition function expanded near the S3/ℤk 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.