Boundary-Boundary Duality on Regular Black Holes, Supersymmetric Solitons and Holographic Spinning Plasma Disks

Abstract

We construct a new family of exact rotating solutions of four-dimensional Einstein--Maxwell theory with negative cosmological constant describing regular spinning AdS black holes and smooth solitons. The geometries are free of curvature singularities and admit open regions of parameter space without closed timelike curves, while supersymmetric limits correspond to causally regular horizonless configurations. A remarkable feature of these solutions is the existence of at least two codimension-one conformal boundaries. The first is Minkowski spacetime, where the expectation value of the energy--momentum tensor describes a finite spinning disk of strongly coupled conformal plasma whose edge rotates at the speed of light. The second boundary is a rotating black-hole geometry with vanishing energy--momentum tensor but non-vanishing Cotton tensor, defining a holographic theory in which the dual graviton is fixed at the boundary. We show that the energy density associated with the dual graviton exactly reproduces that of the plasma after a suitable analytic continuation and the identification of the holographic energy scale with the Lorentz factor of the rotating fluid, providing evidence for a boundary-boundary duality. Indeed, electromagnetic duality exchanges the electric and magnetic currents between the boundary supporting the graviton and that supporting the dual graviton thus providing a generalized mirror symmetry between these boundary theories. Hence, the Lorentz factor is identified with the electromagnetic dual of the renormalization scale. In an appropriate limit, the solutions reduce to the planar Reissner--Nordstr\"om--AdS black hole, whereas the supersymmetric solitons have no regular static limit.