Euclidean black saddles and AdS 4 black holes
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Springer
Received: June 29, 2020 Accepted: August 27, 2020 Published: October 12, 2020
Nikolay Bobev, Anthony M. Charles and Vincent S. Min Institute for Theoretical Physics, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
E-mail: [email protected], [email protected], [email protected] Abstract: We find new asymptotically locally AdS4 Euclidean supersymmetric solutions of the STU model in four-dimensional gauged supergravity. These “black saddles” have an S 1 ×Σg 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 × Σg . 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 wellknown supersymmetric dyonic AdS4 black holes in the STU model. Keywords: AdS-CFT Correspondence, Black Holes in String Theory, Supersymmetric Gauge Theory, M-Theory ArXiv ePrint: 2006.01148
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)073
JHEP10(2020)073
Euclidean black saddles and AdS4 black holes
Contents 1 Introduction
1
2 The topologically twisted index and black saddles 2.1 Field theory 2.2 Gravity
4 4 7 12 12 17 19 21 29
4 Explicit solutions 4.1 Euclidean Romans solutions 4.2 Universal solutions with scalars 4.3 Solutions with flavor charges 4.4 Numerics
34 34 36 43 47
5 Discussion 5.1 An ode to extremization 5.2 Generalizations and open questions
53 53 56
A Conventions
59
B N = 2 gauged supergravity
59
C Euclidean BPS conditions C.1 STU model C.2 Lorentzian ansatz and supersymmetry variations C.3 Euclideanization C.4 Euclidean projectors and BPS equations
62 62 63 65 66
D Deriving the on-shell action
70
–i–
JHEP10(2020)073
3 Supergravity and holography 3.1 Euclidean BPS conditions in the STU model 3.2 UV expansion 3.3 IR expansion 3.4 Holographic renormalization 3.5 The holographic match
1
Introduction
where I = 0, 1, 2, 3 labels the Cartan generators of the global symmetry algebra. A natural question in the context of holography is to find a supergravity dual solution to the deformed ABJM theory on S 1 × 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 In order to achieve this feat fo
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