Constructing and Probing Three-Boundary Booklet Geometries

Yan Liu; Shaodong Zhou

Home/Archive/arXiv

arXiv · 2609.37099

Constructing and Probing Three-Boundary Booklet Geometries

Yan Liu·Shaodong Zhou

View original source ↗Read source document ↗Export metadata ↓

Abstract

Partially entangled thermal states (PETS) provide semiclassical families of black-hole microstates prepared through heavy shell insertions. We extend this shell-state framework and propose three-boundary partially entangled thermal states (PETS$_3$) by replacing the two-index insertion data with a trivalent junction tensor. The corresponding bulk three-boundary booklet geometry is constrained semiclassically by the Israel junction condition, allowing us to identify candidate symmetric and mixed-orientation branches. We verify the self-consistency of this construction by counting states in the symmetric all-black-hole sector. Using a heavy-operator probe, we further estimate the detection-to-universal ratio to be $Z_D/Z_U \simeq 3$, twice the two-boundary value of $3/2$. These results suggest that a fine-tuned probe localized on one boundary can test the proposed three-boundary shell state and potentially distinguish it from its two-boundary counterpart.

Explore related subjects

hep-th gr-qc quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Yan Liu, Shaodong Zhou. 2026-09-29. Constructing and Probing Three-Boundary Booklet Geometries. https://arxiv.org/abs/2609.37099

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Cloud Screening of extremal charged BTZ black hole

We study the instability of a charged scalar field in the near-horizon region of an extremal charged BTZ black hole. The extremal geometry contains an $\mathrm{AdS}_2\times S^1$ throat supported by a constant electric field, which lowers the effective scalar mass and can violate the $\mathrm{AdS}_2$ Breitenlohner--Freedman bound. This identifies an infrared instability of the extremal normal state. We then construct a nearby finite-temperature branch of fully backreacted, source-free, node-free hairy black-hole solutions, thereby establishing the nonlinear continuation of the unstable mode near its onset. The scalar condensate modifies both the Maxwell field and the geometry, while stronger gravitational backreaction lowers the critical temperature and suppresses the condensate amplitude. Near the critical point, the condensate exhibits mean-field scaling. We also develop an effective near-horizon interpretation in terms of electric-flux screening. The exact zero-temperature endpoint of the hairy branch is not determined here and remains an open problem.

hep-th↗

arXiv2026

Emergent States and Algebras from the Double-Scaling limit of Pure States in SYK

Recent work has emphasized a subtlety of large- $N$ limits in AdS/CFT: a sequence of pure states in the microscopic theory need not remain pure with respect to the emergent algebra of observables. We study this phenomenon for Kourkoulou-Maldacena (KM) states in the double-scaling limit of the SYK model, and show that their ensemble-averaged algebraic description depends crucially on which observables survive the limit. For fermionic operators of size $N^{1/2}$, generic operators converge to the usual chord operators of double-scaled SYK. The resulting von Neumann algebra is the standard Type II$_1$ factor, and the KM pure states at infinite temperature converge to the tracial state, so generic probes lose access to microscopic purity. We then identify a class of operators adapted to the KM state that also survives the double-scaling limit. Since the KM state may be viewed as a projection inside the tracial state, these become dressed chord creation and annihilation operators. Once included, the limiting algebra becomes Type I$_\infty$ and the limiting state becomes pure. This gives a concrete example in which adding a sufficiently state-adapted operator to the emergent algebra restores access to the purity of the underlying state. We further show that correlators of the dressed operators admit exact modified chord-diagram rules, derive analytic expressions for uncrossed $2n$-point and crossed four-point functions, analyze their finite-temperature semiclassical and Schwarzian limits, study a deformation of the chord Hamiltonian that produces bound states and extends the correspondence with JT gravity plus an EOW brane to general brane tension, and identify an emergent $U(1)$ symmetry together with its finite-$N$ violation. Finally, we discuss analogies with boundary algebras proposed for black hole interiors and closed universes, and suggest lessons from our construction for both.

hep-th↗

arXiv2026

Localized zero modes enhance massive Casimir interactions

Massive quantum fields ordinarily produce strongly screened Casimir interactions at large separation. We show that a normalisable localised zero mode can change this asymptotic behaviour: it opens an additional interaction channel whose decay is parametrically slower than that due to the exchange of massive quantum fluctuations, even though the continuum itself remains gapped. We demonstrate this mechanism analytically and show that the massive quantum fluctuations provide the local dressing of each object's coupling to the zero-mode fluctuations. The sine-Gordon kink provides an exactly solvable realisation in which the Casimir interaction exhibits the predicted zero-mode-dominated large-distance behaviour, with the enhancement localised around the kink.

hep-th↗