Microcanonical Phases of String Theory on AdS_m x S^n

TL;DR

The paper resolves a puzzle about microcanonical phases of string theory on AdS_m × S^n by showing that the proposed localization transition depends on boundary conditions: conformal (toroidal) boundaries do not induce localization on S^{D-p-2}, and AdS_3 requires a careful mass-background choice that again avoids localization. It analyzes toroidal black holes, AdS_3 geometries, and multi-black-hole configurations to argue that no fragmentation or localization instability arises in near-horizon brane spacetimes. The results clarify the stability of these backgrounds within AdS/CFT and illuminate the corresponding phases in the dual gauge theories, including a localized black hole phase on S^p at strong coupling and its distinctive thermodynamic properties. Overall, the work reconciles the brane near-horizon geometries with stability expectations and outlines the rich phase structure expected at low energies for different boundary topologies.

Abstract

Banks, Douglas, Horowitz and Martinec [hep-th/9808016] recently argued that in the microcanonical ensemble for string theory on AdS_m xS^n, there is a phase transition between a black hole solution extended over the S^n and a solution localized on the S^n. If we think of this AdS_m x S^n geometry as arising from the near-horizon limit of a black m-2 brane, the existence of this phase transition is puzzling. We present a resolution of this puzzle, and discuss its significance from the point of view of the dual m-1 dimensional field theory. We also discuss multi-black hole solutions in AdS.