Euclidean black saddles and AdS4 black holes

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×$$ {\Sigma}_{\mathfrak{g}} $$ Σ 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×$$ {\Sigma}_{\mathfrak{g}} $$ Σ 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.

Supersymmetric solitons and a degeneracy of solutions in AdS/CFT

“…2 In this context, both of these three-dimensional configurations have been considered before: the solution with the constant gauge field was studied in [12] as the bulk dual of this twisted partition function. It was noted in [10] that there is a supersymmetric solution with an R 2 × Σ g near-horizon region -our magnetic flux tube -and that this has the same value for the action as the Romans solution. However, it was not previously appreciated that these solutions compete.…”

“…At this value of Φ, the Poincaré-AdS solution is also supersymmetric. The supersymmetry of the soliton in the Euclidean section has been noted before [10], but we give a slightly more careful analysis taking into account the antiperiodic boundary conditions for the fermions on the φ circle. Our remark is that the supersymmetric soliton solutions are perfectly well behaved in the Lorentzian section.…”

“…It is also interesting to consider the phase structure from a Euclidean perspective, to make contact with previous work on supersymmetric partition functions [13][14][15]17]. Previous work on this area has focused on the Euclidean theory with an S 1 × Σ g boundary, where Σ g is a Riemann surface of genus g > 1, but this was extended to consider genus 1 in [10], corresponding to the case we have considered so far. We will comment on the extension of our discussion to higher genus in section 3.…”

“…They are double analytic continuations of a set of supersymmetric naked singularities identified in four dimensions in [7,8] and in five dimensions in [9]. They were also studied in four dimensional Euclidean space very recently in [10] as an extension of the supersymmetric black holes dual to the twisted supersymmetric index. We add to these previous discussions by emphasizing the previously unnoticed fact that these solutions are perfectly well behaved Lorentzian configurations.…”

Uplifting dyonic AdS4 black holes on seven-dimensional Sasaki-Einstein manifolds

“…Recently, the Euclidean supergravity solutions which are called black saddles were constructed in STU supergravity [50] and their on-shell action was shown to agree exactly with the topologically twisted index of ABJM theory. It is of interest to find black saddle solutions in four-dimensional gauged supergravity constructed in [29] and compare them to AdS 4 black holes constructed in [30] and revisited in this paper.…”