Thermodynamics of accelerating and supersymmetric $AdS_4$ black holes

Abstract

We study the thermodynamics of AdS 4 black hole solutions of Einstein-Maxwell theory that are accelerating, rotating, and carry electric and magnetic charges. We focus on the class for which the black hole horizon is a spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions of D = 11 supergravity that are free from conical singularities. We use holography to calculate the Euclidean on-shell action and to define a set of conserved charges which give rise to a first law. We identify a complex locus of supersymmetric and nonextremal solutions, defined through an analytic continuation of the parameters, upon which we obtain a simple expression for the on-shell action. A Legendre transform of this action combined with a reality constraint then leads to the Bekenstein-Hawking entropy for the class of supersymmetric and extremal black holes.

D4-branes wrapped on a spindle

“…Finally, as an important step towards improving control on the dual field theories, it would be worthwhile computing an appropriately regularised on-shell action, that should prove the validity of our conjectural off-shell free energy (4.18). To do this, one may need to know the full "black two-brane" solution, interpolating between AdS 6 asymptotically and AdS 4 × Σ in the near-horizon, similarly to [19]. However, it may be possible to employ the strategy of [25] to prove that the supergravity (Euclidean) on-shell action localises at the poles of the spindle, which are the fixed points for the canonical Killing vector field associated to any (Euclidean) supersymmetric solution of the theory [46].…”

“…which coincides with the entropy in [12] upon setting σ = −1. In minimal D = 4 gauged supergravity the entropy function (5.15), for ϕ 1 = ϕ 2 and n 1 = n 2 , was derived in [19],…”

“…For theories in d = 4 and d = 6 this lack of knowledge can be bypassed employing the recipe of [8] for extracting the trial central charge of the (d − 2)-dimensional theories from the anomaly polynomials of the parent theories. In d = 3 an entropy function was obtained in [19], from the on-shell gravitational action of the suitably regularised black hole solutions, employing the method of [20]. Extremizing this reproduces the entropy associated to the AdS 2 × Σ solution of [7].…”

M2-branes wrapped on a topological disk

“…First, there are AdS solutions from branes wrapped on a spindle which is topologically a two-sphere with orbifold singularities at the poles. The AdS solutions from D3-branes, [6,7,8], M2-branes, [9,10], and M5-branes, [11], wrapped on a spindle are recently found. Although the solutions from D3-branes were previously found in [12,13,14,15,16] in diverse contexts, the interpretation as a spindle and their AdS/CFT correspondence are new.…”

Five-branes wrapped on topological disks from 7D N=2 gauged supergravity

“…Recently, new classes of AdS × Σ solutions, in which unbroken supersymmetry is not realized by a topological twist, have been found for Σ being a two-dimensional space with non-constant curvature. These solutions describe supersymmetric branes wrapped on a spindle, which is topologically a two-sphere with orbifold singularities at the poles, [30,31,32,33,34,35,36], see also [37] for a more recent result, or on a topological disk with non-trivial U(1) holonomy on the boundary or "half-spindle" [38,39,40,41,42,43]. These lead to new supersymmetric AdS geometries from gauged supergravities which are dual to lower-dimensional SCFTs arising from compactifications of higher-dimensional SCFTs on a spindle or a half-spindle.…”