A nAttractor Mechanism for nAdS(2)/nCFT(1) Holography

TL;DR

The paper develops the gravitational side of the proposed nAdS$_2$/nCFT$_1$ duality for nearly extremal black holes in four-dimensional $N=2$ supergravity by introducing the nAttractor mechanism, which expresses near-horizon data of near-extremal solutions in terms of derivatives of extremal attractor data with respect to charges. It shows that departures from extremality can be captured by a controlled perturbation of the BPS flow, yielding a simple, charge-derivative formula for the symmetry-breaking scale $L$ and clarifying how multiple moduli-induced scales enter the near-horizon theory. The analysis treats generic vector-multiplet moduli and specializes to explicit STU black holes, obtaining concrete expressions for the symmetry-breaking scales and linking them to the long-string picture in certain limits. These results illuminate how holographic IR physics in AdS$_2$ regions encodes the UV data of moduli and charges, providing a practical framework to compute near-horizon deformations without full black hole solutions and clarifying the role of multiple scales in nAdS$_2$/nCFT$_1$ holography.

Abstract

We study the nearly AdS(2) geometry of nearly extremal black holes in N = 2 supergravity in four dimensions. In the strictly extreme limit the attractor mechanism for asymptotically flat black holes states that the horizon geometries of these black holes are independent of scalar moduli. We determine the dependence of the near extreme geometry on asymptotic moduli and express the result in simple formulae that generalize the extremal attractor mechanism to nearly extreme black holes. This is a nAttractor mechanism. We discuss the dependence of the near horizon theory on the scales introduced by generic attractor flows.