Phase transitions of neutral planar hairy AdS black holes
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Springer
Received: December Revised: May Accepted: June Published: July
11, 30, 13, 20,
2019 2020 2020 2020
Andres Anabalon,a Dumitru Astefanesei,b David Choquea,c,e and Jose D. Edelsteind a
Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ib´ an ˜ez, Av. Padre Hurtado 750, Vi˜ na del Mar, Chile. b Instituto de F´ısica, Pontificia Universidad Cat´ olica de Valpara´ıso, Casilla 4059, Valpara´ıso, Chile c Universidad T´ecnica Federico Santa Mar´ıa, Av. Espa˜ na 1680, Valpara´ıso, Chile d Departamento de F´ısica de Part´ıculas & Instituto Galego de F´ısica de Altas Enerx´ı as (IGFAE), Universidad de Santiago de Compostela, E-15782 Santiago de Compostela, Spain e Universidad Nacional de San Antonio Abad del Cusco, Av. La Cultura 733, Cusco, Per´ u
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We investigate the phase diagram of a general class of 4-dimensional exact regular hairy planar black holes. For some particular values of the parameters in the moduli potential, these solutions can be embedded in ω-deformed N = 8 gauged supergravity. We construct the hairy soliton that is the ground state of the theory and show that there exist first order phase transitions. Keywords: AdS-CFT Correspondence, Black Holes ArXiv ePrint: 1912.03318
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)129
JHEP07(2020)129
Phase transitions of neutral planar hairy AdS black holes
Contents 1
2 Exact hairy AdS soliton solutions 2.1 The AdS soliton 2.2 The hairy AdS soliton 2.3 The Euclidean action of the hairy black hole 2.4 The Brown-York stress tensor 2.5 The Euclidean action of the hairy AdS soliton
4 4 5 6 7 8
3 Phase transitions 3.1 First order phase transitions 3.2 Phase transitions in ω-deformed N = 8 supergravity 3.3 M-theory embedding
9 9 13 14
4 Holography of hairy planar solutions
15
5 Stability of the hairy solitons
16
6 Conclusions and further directions
17
1
Introduction
The AdS/CFT correspondence [1] enables us to understand phases of strongly coupled gauge theories as well as their phase transitions from a dual perspective. Famously enough, Hawking and Page showed [2] that there exists a phase transition between spherical AdS (Schwarzschild) black hole and global AdS spacetime. Above the critical temperature, Tc , the black hole becomes thermodynamically stable while below Tc it is unstable, global AdS being energetically favorable. Within the AdS/CFT duality this corresponds to a confinement/deconfinement phase transition in the dual quantum field theory [3]. On the Euclidean section there are two scales: the temperature (related to the periodicity of the Euclidean time, β) and the radius of the 3-sphere, β 0 . The black hole represents a thermal state in the field theory and so, due to conformal invariance, only the ratio β/β 0 is relevant for the phase transition of the dual gauge theory on S 3 × S 1 . The phase transition is sensitive to the topology of spacetime,
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