ABJM at finite $N$ via 4d supergravity

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.

7 pages; v2 improved discussion; v3 short outlook added

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Cited by in corpus (10)

• Large $N$ Partition Functions of the ABJM Theory
• Large $N$ Superconformal Indices for 3d Holographic SCFTs
• Boundary terms and conserved charges in higher-derivative gauged supergravity
• On curvature-squared invariants of minimal five-dimensional supergravity from superspace
• Hyper-Dilaton Weyl Multiplets of 5D and 6D Minimal Conformal Supergravity
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• Microscopics of de Sitter Entropy from Precision Holography
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• Six-dimensional $\mathcal{N}=(2,0)$ Conformal Superspace