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.
An Airy Tale at Large $N$
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study the sphere partition function of 3d $\mathcal{N}=2$ holographic SCFTs arising on the worldvolume of $N$ coincident M2-branes in the presence of squashing and real mass deformations. We argue that the all-order large $N$ perturbative expansion of the partition function resums into a compact expression in terms of an Airy function. We provide ample evidence for this conjecture using numerical methods, saddle point analysis in the 't Hooft limit, and the relation of the squashed sphere partition function to the Cardy-like limit of the superconformal index. We also discuss the relation of our results to topological string theory and the statistical mechanics of Fermi gases. Our conjecture has a bearing on the AdS/CFT correspondence and the structure of perturbative M-theory corrections to 11d supergravity which we discuss.
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hep-th 8years
2026 8representative citing papers
Finite-N indices for M5- and M2-branes are expressed via the same equivariant characteristic classes, generalizing M2/M5 duality through geometry exchange.
Derives Airy representation for S^3 partition functions in M2-brane theories that exactly matches equivariant topological string predictions and proposes a new CY4 to C x CY3 correspondence via quantum curves.
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.
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
Vertices of fundamental domains for del Pezzo quantum curves with FI parameters are realized as factorized curves from 5-branes dressed by FI parameters, matching minuscule weights.
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.
The complex saddles of the ABJM index are interpreted through instability of wrapped M5-branes in the dual gravity theory.
citing papers explorer
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Holographic Tests of the $\mu$ Ensemble
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.
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Indices of M5 and M2 branes at finite $N$ from equivariant volumes, and a new duality
Finite-N indices for M5- and M2-branes are expressed via the same equivariant characteristic classes, generalizing M2/M5 duality through geometry exchange.
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$S^3$ partition functions and Equivariant CY$_4 $/CY$_3$ correspondence from Quantum curves
Derives Airy representation for S^3 partition functions in M2-brane theories that exactly matches equivariant topological string predictions and proposes a new CY4 to C x CY3 correspondence via quantum curves.
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Bootstrapping ABJM theory
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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Towards OSV in AdS
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
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Factorized Quantum Curves and Minuscule Vertices in 3D Duality Cascades with FI Parameters
Vertices of fundamental domains for del Pezzo quantum curves with FI parameters are realized as factorized curves from 5-branes dressed by FI parameters, matching minuscule weights.
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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.
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A gravity interpretation for the complex Euclidean saddles of the ABJM index
The complex saddles of the ABJM index are interpreted through instability of wrapped M5-branes in the dual gravity theory.