Holographic boundary states and dimensionally-reduced braneworld spacetimes

TL;DR

This work builds a concrete bridge between holographic braneworld cosmologies and microscopic boundary states in a complex SYK model. By showing that boundary states in cSYK look thermal with a fixed charge, and that their dynamics matches a dimensionally reduced JT gravity description with an ETW particle, the authors provide explicit evidence for a microscopic realization of ETW-brane spacetimes. The dual pictures share the same Schwarzian-dominated dynamics and symmetry-breaking pattern, reinforcing the AdS/BCFT-inspired holographic framework. Although the setup does not locally localize gravity, it offers a tractable arena to explore cosmological holography, bulk-boundary correspondences, and the role of boundary conditions in distinguishing microstates via bulk trajectories and boundary observables.

Abstract

Recently it was proposed that microscopic models of braneworld cosmology could be realized in the context of AdS/CFT 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 AdS/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.

Figures (17)

• Figure 1: Single fermion two-point functions. The left hand sides and right hand sides of equation (\ref{['2pf4pf']}) are plotted along with the thermal two-point function in the corresponding charge subsector for $N=8$, $k=1$ and a single realization of the Hamiltonian. The expectations outlined in Section \ref{['singlefermionsection']} are matched to good accuracy. Note that for $\tau_1 \approx \tau_2=0$ the thermal two-point function correctly takes the value $G(0^\pm,0)\approx \mathcal{Q}/N\mp 1/2$. (a) $\mathcal{Q}=0$, $\beta=2\tau_0=1$. (b) $\mathcal{Q}=-2$, $\beta=2\tau_0=1$. (c) $\mathcal{Q}=0$, $\beta=2\tau_0=100$.
• Figure 2: Collective two-point functions. The left hand side and right hand side of equation (\ref{['coll2pf']}) are plotted for $N=8$, $k=1$ and a single realization of the Hamiltonian. The expectations outlined in Section \ref{['collectivesection']} are matched to good accuracy. Note that for $\tau_1 \approx \tau_2=0$ the collective and the thermal two-point functions correctly take the value $G(0^\pm,0)\approx \mathcal{Q}/N\mp 1/2$. (a) $\mathcal{Q}=0$, $\beta=2\tau_0=1$. (b) $\mathcal{Q}=-2$, $\beta=2\tau_0=1$. (c) $\mathcal{Q}=0$, $\beta=2\tau_0=100$.
• Figure 3: Boundary states and canonical ensemble. The symmetry breaking pattern we encountered when evaluating correlators over a boundary state can be visualized by considering the thermal circle with length $\beta=2\tau_0$ with a fixed, special point at $\tau=\pm\tau_0$. The physics in a boundary state will then be equivalent to the one described by the canonical ensemble at fixed charge in the same charge subsector, except the collective fields must satisfy the appropriate boundary conditions at the special point.
• Figure 4: Trajectory of the brane in the Euclidean wormhole. The angular coordinate is the Euclidean time $\tau$ and the radial coordinate is the radius $r$. The central point represents the outer horizon $r=r_+$ and the circumference is the asymptotic AdS boundary. Each point in the diagram is a $(d-1)$-dimensional sphere. The ETW brane contracts from the boundary to a minimum radius $r_0$ at $\tau=\pm\beta/2$, and then expands back to the boundary. The red region is outside the ETW brane and therefore is not part of the geometry.
• Figure 5: Trajectory of the brane in Lorentzian signature. The brane emerges from the past horizon in the left asymptotic region and collapses into the future horizon. The red region, including the left asymptotic boundary, is cut off by the ETW brane and is not part of the geometry. We glued here more patches of the AdS-RN spacetime, extending the trajectory of the brane. However, the trajectory is reliable only between the intersection points of the brane with the (inner) Cauchy horizon.