Abstract
Recently it was proposed that microscopic models of braneworld cosmology could be realized in the context of anti--de Sitter/conformal field theory ($\mathrm{AdS}/\mathrm{CFT}$) correspondence using black hole microstates containing an end-of-the-world brane. Motivated by a desire to establish the microscopic existence of such microstates, which so far have been discussed primarily in bottom-up models, we have studied similar microstates in a simpler version of $\mathrm{AdS}/\mathrm{CFT}$. On one side, we define and study boundary states in the charged Sachdev-Ye-Kitaev model and show that these states typically look thermal with a certain pattern of symmetry breaking. On the other side, we study the dimensional reduction of microstates in Einstein-Maxwell theory featuring an end-of-the-world brane and show that they have an equivalent description in terms of 2D Jackiw-Teitelboim gravity coupled to an end-of-the-world particle. In particular, the same pattern of symmetry breaking is realized in both sides of the proposed duality. These results give significant evidence that such black hole microstates have a sensible microscopic realization.
Highlights
The anti–de Sitter/conformal field theory (AdS=CFT) correspondence [1,2,3,4] is one of the most promising frameworks for the formulation of a quantum theory of gravity
Inspired by the AdS/BCFT proposal [7,8,9], one possible answer was provided by the holographic braneworld cosmology models recently proposed in [10,11]
In analogy with the Majorana SYK case [21], we show that charged Sachdev-Ye-Kitaev (cSYK) boundary states look thermal with inverse temperature β 1⁄4 2τ0 and with properties analogous to those described by the canonical ensemble for a fixed-charge superselection sector
Summary
The anti–de Sitter/conformal field theory (AdS=CFT) correspondence [1,2,3,4] is one of the most promising frameworks for the formulation of a quantum theory of gravity. We show that configurations where the brane is tangent to the regularized boundary and the Schwarzian fluctuations of the boundary preserve such intersection point exhibit exactly the same pattern of symmetry breaking that we observe in the cSYK boundary states These results provide strong evidence for the duality between asymptotically AdS black holes containing an ETW brane and pure boundary states in a dual quantum mechanical theory, thereby realizing explicitly a simplified version of the holographic braneworld cosmology proposals [10,11]. The holographic description of spacetimes with branes that are far from the black hole horizon and can localize gravity likely requires more complicated boundary states of higherdimensional CFTs such as N 1⁄4 4 SYM [15].
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