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.
ABJM at finite N via 4d supergravity
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We apply the conjecture of arXiv:2111.06903 for gravitational building blocks to the effective supergravity description of M-theory on S$^7/\mathbb{Z}_k$. Utilizing known localization results for the holographically dual ABJM theory, we determine a complete tower of higher derivative corrections to the AdS$_4$ supergravity and a further set of quantum corrections. This uniquely fixes the gravitational block, leading to holographic predictions for a number of exact ABJM observables, excluding only constant and non-perturbative corrections in the gauge group rank $N$. The predicted S$^3$ partition function is an Airy function that reproduces previous results and generalizes them to include arbitrary squashing and mass deformations/R-charge assignments. The topologically twisted and superconformal indices are instead products of two different Airy functions, in agreement with direct numeric calculations in the unrefined limit of the former object. The general fixed-point formula for an arbitrary supersymmetric background is similarly given as a product of Airy functions.
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hep-th 5years
2026 5representative citing papers
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.
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.
Equivariantly closed forms in D=4 N=2 conformal supergravity allow closed-form supersymmetric observables in higher derivative theories without solving equations of motion.
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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$S^3$ 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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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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Equivariant localization for higher derivative supergravity
Equivariantly closed forms in D=4 N=2 conformal supergravity allow closed-form supersymmetric observables in higher derivative theories without solving equations of motion.