Abstract
We find new asymptotically locally AdS4 Euclidean supersymmetric solutions of the STU model in four-dimensional gauged supergravity. These “black saddles” have an S1× {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 S1× {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 AdS4 black holes in the STU model.
Highlights
A fundamental entry in the holographic dictionary is the map between the on-shell action of an asymptotically locally AdS gravitational solution and the path integral of the dual quantum field theory
The Euclidean black saddle solution space contains special points that can be Wick-rotated to regular Lorentzian supergravity backgrounds that correspond to the wellknown supersymmetric dyonic AdS4 black holes in the STU model
To study the topologically twisted index in a holographic setting we focus on the ABJM theory which has a well-known holographic dual in terms of the AdS4 × S7/Zk solution of M-theory [5]
Summary
A fundamental entry in the holographic dictionary is the map between the on-shell action of an asymptotically locally AdS gravitational solution and the path integral of the dual quantum field theory. A natural question in the context of holography is to find a supergravity dual solution to the deformed ABJM theory on S1 × Σg and compute the partition function (1.1) in terms of its on-shell action This question was studied in detail in [6] where it was shown that the topologically twisted index (1.1) accounts for the Bekenstein-Hawking entropy of the supersymmetric asymptotically AdS4 static black hole solutions of gauged supergravity found in [7].1. To establish that the black saddle supergravity solutions provide the holographic dual description of the topologically twisted ABJM theory on S1 × Σg for general values of (u, p) we show that their regularized on-shell action agrees with the supersymmetric localization result in (1.1). In the appendices we summarize our supergravity notation and conventions and present the details of the derivation of the BPS equations and the calculation of the on-shell action of the black saddle solutions
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