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ABJM at finite $N$ via 4d supergravity
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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.
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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Six-dimensional $\mathcal{N}=(2,0)$ Conformal Superspace
A new off-shell 6D N=(2,0) conformal superspace is constructed, and its unique Bach tensor superfield is derived up to overall scaling.
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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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