Exact Planar Black Hole in AdS-Einstein-Scalar Gravity with IR-Emergent Nearly Conformal Fluid

Abstract

We study an exact analytic solution describing a static plane-symmetric hairy black hole in four-dimensional Einstein gravity minimally coupled to a neutral scalar, arising as a consistent truncation of type IIA supergravity on AdS$_4\times\mathbb{CP}^3$, the compactification dual to the strongly coupled thermal dynamics of the ABJM theory. The solution is characterized by two independent parameters. We perform the thermodynamic description by treating the scalar hair parameter as an independent variable, deriving the generalized first law and verifying the Euler relation. The UV boundary theory is a three-dimensional QFT at finite temperature deformed by an effectively marginally relevant scalar operator with logarithmic RG flow. The boundary theory exhibits explicit scale-symmetry breaking at high energies but recovers the behavior of a conformal fluid in the infrared thermal limit.