3D τRR-minimization in AdS4 gauged supergravity

In this paper we propose the identification in AdS(4) N = 2 gauged supergravity of the coefficient tau(RR) of 3D N = 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 TRR-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.