Near-extremal vanishing horizon AdS5 black holes and their CFT duals

We consider families of charged rotating asymptotically AdS5 Extremal black holes with Vanishing Horizon (EVH black holes) whose near horizon geometries develop locally AdS3 throats. Using the AdS3/CFT2 duality, we propose an EVH/CFT2 correspondence to describe the near-horizon low energy IR dynamics of near-EVH black holes involving a specific large N limit of the 4d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N}=4 $\end{document} SYM. We give a map between the UV and IR near-EVH excitations, showing that the ‘UV first law’ of thermodynamics reduces to the ‘IR first law’ satisfied by the near horizon BTZ black holes in this near-EVH limit. We also discuss the connection between our EVH/CFT proposal and the Kerr/CFT correspondence in the cases where the two overlap.