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Large $N$ Partition Functions of the ABJM Theory
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abstract
We study the large $N$ limit of some supersymmetric partition functions of the $\mathrm{U}(N)_{k}\times \mathrm{U}(N)_{-k}$ ABJM theory computed by supersymmetric localization. We conjecture an explicit expression, valid to all orders in the large $N$ limit, for the partition function on the $\mathrm{U}(1)\times \mathrm{U}(1)$ invariant squashed sphere in the presence of real masses in terms of an Airy function. Several non-trivial tests of this conjecture are presented. In addition, we derive an explicit compact expression for the topologically twisted index of the ABJM theory valid at fixed $k$ to all orders in the $1/N$ expansion. We use these results to derive the topologically twisted index and the sphere partition function in the 't Hooft limit which correspond to genus $\tt g$ type IIA string theory free energies to all orders in the $\alpha'$ expansion. We discuss the implications of our results for holography and the physics of AdS$_4$ black holes.
Forward citations
Cited by 7 Pith papers
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Airy functions from quantum M-theory
Relative equivariant localization of quantum M-theory reproduces the Airy partition functions of ABJM and toric Calabi-Yau M2-brane theories, up to prefactor and non-perturbative corrections.
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Equivariant localization for $D=4$ gauged supergravity
Supersymmetric Euclidean D=4 N=2 gauged supergravity actions and fluxes localize onto R-symmetry fixed points, proving large-N SCFT free-energy formulas and UV-IR relations.
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Constants in Sequences of M2-brane Partition Functions
The N-independent constants of the ABJM and ADHM Bethe potentials and of the ABJM twisted index are expressed as finite combinations of the constant map function A.
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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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Ensembles in M-theory and Holography
The M2-brane partition function should be viewed as a grand canonical object in AdS4/ABJM holography, fixing the three-form source rather than the flux number N, which resolves puzzles about Airy shifts and one-loop e...
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An Airy Tale at Large $N$
The paper presents numerical and analytic evidence that the large-N sphere partition function of five classes of M2-brane SCFTs, with squashing and real masses, takes the form of an Airy function to all orders in 1/N.
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Perturbatively exact supersymmetric partition functions of ABJM theory on Seifert manifolds and holography
A perturbatively exact ABJM partition function on Seifert manifolds is matched to Euclidean AdS-Taub-Bolt supergravity, including N^{1/2} and log N corrections.
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