3D ${\tau }_{RR}$-minimization in AdS${}_4$ gauged supergravity

Abstract

In this paper we propose the identification in AdS4 N = 2 gauged supergravity of the coefficient ${\tau }_{RR}$ of 3D N = 2 SCFTs. We constraint 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 in the special geometry. We identify this mechanism with the supergravity dual of the ${\tau }_{RR}$-minimization. We check this proposal in the ABJM model, comparing with the expectations from localization and the AdS/CFT duality. We comment also on some possible relations with the black hole microstate counting, recently obtained from the application of localization techniques.

19 pages

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• Holographic renormalization group flows in two-dimensional gravity and $AdS$ black holes