Black hole bound states in AdS_3 x S^2

TL;DR

The paper constructs and analyzes a large family of supersymmetric bound-state geometries in AdS3 × S2 that are dual to sectors of the 1+1D (0,4) MSW CFT arising from wrapped M5-branes. It develops a systematic decoupling limit from 4D/5D multicenter solutions, establishes a attractor-flow-based existence criterion for these AdS3 × S2 geometries, and shows that entropy can be dominated by either BTZ-like black holes or localized BMPV-type holes on the S2, signifying a supersymmetric Entropy Enigma and phase transitions. A detailed mapping to CFT data is provided, including central charges, L0, and SU(2)_R charges, and a nuanced discussion of the MSW string content and possible RG behavior. The work highlights how walls of stability and decoupled AdS throats reshape the dual CFT interpretation and raises important questions about the full CFT dual of multi-centered bound states, the role of moduli, and the quantization of solution spaces. Overall, it links intricate gravity solutions to nuanced 0,4 CFT dynamics and motivates further exploration of CFT density matrices and microstate counting in AdS3 × S2 geometries.

Abstract

We systematically construct the geometries dual to the 1+1 dimensional (0,4) conformal field theories that arise in the low-energy description of wrapped M5-branes in S^1 x CY_3 compactifications of M-theory. This includes a large number of multicentered black hole bound states asymptotic to AdS_3 x S^2. In addition, we find many geometries that develop multiple, mutually decoupled AdS_3 x S^2 throats. We argue there is a useful one to one correspondence between the connected components of the space of solutions and particular limits of type IIA attractor flow trees. We point out that there is a thermodynamic instability of small supersymmetric BTZ black holes to localization on the S^2, a supersymmetric and exactly solvable analog of the well known AdS-Schwarzschild localization instability, and identify this with the ``Entropy Enigma'' in four dimensions. We discuss the phase transition this suggests, and initiate the CFT interpretation of these results.