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.
Euclidean Black Saddles and AdS$_4$ Black Holes
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We find new asymptotically locally AdS$_4$ Euclidean supersymmetric solutions of the STU model in four-dimensional gauged supergravity. These "black saddles" have an $S^1\times \Sigma_{\mathfrak{g}}$ boundary at asymptotic infinity and cap off smoothly in the interior. The solutions can be uplifted to eleven dimensions and are holographically dual to the topologically twisted ABJM theory on $S^1\times \Sigma_{\mathfrak{g}}$. We show explicitly that the on-shell action of the black saddle solutions agrees exactly with the topologically twisted index of the ABJM theory in the planar limit for general values of the magnetic fluxes, flavor fugacities, and real masses. This agreement relies on a careful holographic renormalization analysis combined with a novel UV/IR holographic relation between supergravity parameters and field theory sources. The Euclidean black saddle solution space contains special points that can be Wick-rotated to regular Lorentzian supergravity backgrounds that correspond to the well-known supersymmetric dyonic AdS$_4$ black holes in the STU model.
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hep-th 3years
2026 3roles
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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.
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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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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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.