The Gravitational Description of Coarse Grained Microstates

TL;DR

This work builds a precise map from 1/2-BPS D1-D5 microstates to half-BPS Type IIB supergravity geometries by associating CFT density matrices to phase-space densities over loops in ${\mathbb R}^4$ and constructing the corresponding harmonic functions that define the 10D metric. Through coherent-state intuition and careful treatment of fixed-length constraints, the authors demonstrate how gravity emerges from coarse graining over microstates and explicitly realize geometries for conical defects, the M=0 BTZ black hole, and small black rings, including quantum smearing effects that vanish as $N/k\to\infty$. They show that coarse-grained ensembles yield a universal geometric description parameterized by a few macroscopic quantities, and they find a stretched-horizon entropy that typically scales as $N^{3/4}$—larger than the microstate entropy $\sim N^{1/2}$—highlighting subtleties in relating microstate counting to geometric entropy. The results support the fuzzball/no-hair perspective in AdS$_3$/CFT$_2$, elucidate the role of kinetic and dipole data in the bulk, and suggest promising directions for extending to less supersymmetric cases and connecting to CFT one-point functions.

Abstract

In this paper we construct a detailed map from pure and mixed half-BPS states of the D1-D5 system to half-BPS solutions of type IIB supergravity. Using this map, we can see how gravity arises through coarse graining microstates, and we can explicitly confirm the microscopic description of conical defect metrics, the M=0 BTZ black hole and of small black rings. We find that the entropy associated to the natural geometric stretched horizon typically exceeds that of the mixed state from which the geometry was obtained.