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 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 (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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- AdS-CFT Correspondence