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

TL;DR

This paper proposes a supergravity-based method to determine the exact R-charge in 3D N=2 SCFTs by minimizing a specific coefficient, linking holography, localization, and black hole microstate counting.

Contribution

It introduces a novel $ au_{RR}$-minimization principle in AdS4 N=2 gauged supergravity, connecting supergravity scalar attractors with field theory R-charge determination.

Findings

The $ au_{RR}$ function is minimized by the exact R-charge.

The mechanism is validated in the ABJM model.

Potential links to black hole microstate counting are discussed.

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.