3D τRR-minimization in AdS4 gauged supergravity

In this paper we propose the identification in AdS4N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 gauged supergravity of the coefficient τRR of 3D N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 SCFTs. We constrain the structure of this function in supergravity by combining the results from unitarity, holography and localization. We show that our conjectured function is minimized by the exact R-charge, corresponding to a gravitational attractor for the scalars of special geometry. We identify this mechanism with the supergravity dual of τRR-minimization. We check this proposal in ABJM model, comparing with expectations from localization and AdS/CFT duality. We comment also on possible relations with black hole microstates counting, recently obtained from application of localization techniques.