Abstract
We investigate the emergence of de Sitter geometry from quantum coherence effects in boundary-state constructions. A mesoscopic D-brane is defined as a finite-level wavepacket superposition of Ishibashi states satisfying projected Virasoro gluing conditions, with a truncation error that is exponentially small in the cutoff. Mesoscopic truncation introduces a finite spectral bandwidth in the closed-string channel, and coherence phases across a brane stack reorganize the spectral weight seen by probe two-point functions.We consider a heavy scalar probe operator and derive, from a positive spectral representation, the large-separation asymptotic formC(X,Y)∼A(X,Y)exp(−mℓeff(X,Y)),where ℓeff is an emergent length functional determined by the spectral structure of the mesoscopic state. In an exactly solvable realization — level-truncated Dirichlet boundary states of a compact free boson — the spectral weights are obtained in closed form: a critical stack coherence phase deletes the lowest spectral band identically, generating a correlation length ξ=R2 (units α′=2) that is independent of the cutoff, while the delocalized limit restores scale-invariant decay with the free critical exponent.Defining an effective distance from the correlator and employing Synge’s world-function identity, we reconstruct the local metric on the manifold of probe-insertion labels. The de Sitter branch is identified by an intrinsic curvature criterion — constant positive curvature of the reconstructed metric — from which the invariant distance ℓeff=Larcosh(Z) and the static-patch metricds2=−(1−r2L2)dt2+dr21−r2/L2+r2dΩd−12follow by the rigidity of constant-curvature geometries rather than by assumption; the horizon scale L is set by the mesoscopic spectral data. In a two-dimensional worked example we solve the corresponding inverse problem explicitly: brane-stack coherence data are exhibited whose emergent lapse matches the de Sitter form, on label settings independent of the design, with root-mean-square accuracy 3.6×10−4, the independently computed curvature being constant at the corresponding accuracy.Our results provide a concrete, falsifiable mechanism by which quantum coherence properties of boundary states generate an emergent de Sitter geometry, and quantify how correlation length, spectral structure, and horizon scale are dynamically linked.