Fixed-μ ensemble computations in 11d supergravity reproduce ABJM partition functions (squashed S³, SCI, TTI) as Airy functions via a Laplace transform whose measure is fixed by bulk zero-mode counting.
Instanton contributions to the ABJM free energy from quantum M2 branes
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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 $F^{\rm inst}(N,k) = - ({\sin^{2} \frac{2\pi}{k}} )^{-1} \, \exp (-2\pi \sqrt\frac{2N}{k}) + \cdots$ . The exponent comes from the action of an M2 brane instanton wrapped on $S^3/{\mathbb Z}_k$, which represents the M-theory uplift of the $\mathbb{C}P^1$ instanton in type IIA string theory on AdS$_4 \times \mathbb{C}P^3$. 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 $({\sin^{2} \frac{2\pi}{k}})^{-1} $ is reproduced by the 1-loop term in the M2 brane partition function expanded near the $S^3/\mathbb{Z}_k$ 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.
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hep-th 5years
2026 5representative citing papers
A bootstrap approach applied to ABJM theory yields analytic derivations of instanton corrections to the free energy and to 1/2 and 1/6 BPS Wilson loops, confirming relations previously known only conjecturally.
The 1-loop M2-brane correction to the AdS2 imes S1 Wilson-loop partition function in AdS3 imes S3 imes T5 is exactly κ/√(2π) with no subleading 1/κ series.
BPS conditions for M2-branes wrapping cycles in weak G2 manifolds are equivalent to associativity, with one-loop effects for invariant cycles in Sasaki-Einstein orbifolds expressed via equivariant indices and recovering known S3/Zk results.
New framework for one-loop log divergences on AdS x S spaces recovers the 1/4 log N ABJM correction from 11d SUGRA in 4d language.
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A bootstrap approach applied to ABJM theory yields analytic derivations of instanton corrections to the free energy and to 1/2 and 1/6 BPS Wilson loops, confirming relations previously known only conjecturally.
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Wilson loop in AdS$_3 \times S^3 \times T^4$ from quantum M2 brane
The 1-loop M2-brane correction to the AdS2 imes S1 Wilson-loop partition function in AdS3 imes S3 imes T5 is exactly κ/√(2π) with no subleading 1/κ series.
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Membrane instantons and non-perturbative effects in $\mathrm{AdS}_{4}/\mathrm{CFT}_{3}$
BPS conditions for M2-branes wrapping cycles in weak G2 manifolds are equivalent to associativity, with one-loop effects for invariant cycles in Sasaki-Einstein orbifolds expressed via equivariant indices and recovering known S3/Zk results.
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One-loop divergences for KK theories on $\mathrm{AdS}\times S$ spaces; a reanalysis of $\mathrm{AdS}_4 \times S^7\,\big/$ ABJM precision holography
New framework for one-loop log divergences on AdS x S spaces recovers the 1/4 log N ABJM correction from 11d SUGRA in 4d language.