Hair-brane Ideas on the Horizon

TL;DR

This paper develops a bridge between horizonless microstate geometries and black hole entropy by focusing on branes that wrap degenerate cycles as charge centers approach each other. It arguing that light W-branes appear on the Coulomb/Higgs branches, and that a truncated quiver quantum mechanics model can capture a nontrivial fraction of the BPS entropy, with the quiver state counting scaling in the same way as the BH entropy under charge rescaling. The authors derive the brane dynamics in M-theory and type IIB frames, relate M2-brane and D3-brane probes to Landau-level degeneracies, and show that the horizon region can be interpreted as a condensate of stretched branes wrapping vanishing cycles, potentially realizing the AdS$_3$ long string on the gravity side. While the quiver truncation does not exhaust all microstate degrees of freedom, the results provide a concrete, computable sector whose entropy scales consistently with the three-charge BH entropy and offer a concrete framework for understanding how hair-brane dynamics may resolve aspects of the information problem in AdS$_3$ contexts.

Abstract

We continue an examination of the microstate geometries program begun in arXiv:1409.6017, focussing on the role of branes that wrap the cycles which degenerate when a throat in the geometry deepens and a horizon forms. An associated quiver quantum mechanical model of minimally wrapped branes exhibits a non-negligible fraction of the gravitational entropy, which scales correctly as a function of the charges. The results suggest a picture of AdS_3/CFT_2 duality wherein the long string that accounts for BTZ black hole entropy in the CFT description, can also be seen to inhabit the horizon of BPS black holes on the gravity side.

Figures (4)

• Figure 1: A D2-brane fractionates on a stack of D4-branes. U-duality and scaling limits relate this situation to both $AdS_3\times\mathbb{S}^3\times\mathbb{T}^4$ and little string theory.
• Figure 2: Examples of source configurations for two-charge solutions. (Left) The black curve results from a macroscopic number of quanta in the lowest mode; it sources a geometry which is a spectral flow of the global $AdS_3\times\mathbb{S}^3$ geometry. On the other hand, putting a single quantum in the highest available mode (the tightly coiled spiral shown in red) makes an orbifold geometry $(AdS_3\times \mathbb{S}^3)/\mathbb{Z}_{n_1n_5}$. (Right) An NS5-P supertube separates the individual fivebranes onto the Coulomb branch by a fixed amount determined by the momentum charge.
• Figure 3: Scaling together a cluster of poles leads to a throat whose depth is controlled by the size of the cluster $\rho_{\rm min}$ relative to its distance $\rho_{\rm max}$ to other poles.
• Figure 4: Poles in the the metric function $V$ cause the degeneration of the $\mathbb{S}^1_\psi$ fiber of the Gibbons-Hawking base ${\cal B}_4$. Each pair of points defines a two-cycle characterized by $\mathbb{S}^1_\psi$ fibered over a path ${\cal C}_{ab}$ between poles ${\bf y}_a$ and ${\bf y}_b$.