PHYSICAL REVIEW D 112, 126002 (2025)
Dongsu Bak ,1,* Chanju Kim ,2,† and Sang-Heon Yi 1,‡
1Physics Department and Natural Science Research Institute, University of Seoul, Seoul 02504 Korea
2Department of Physics, Ewha Womans University, Seoul 03760 Korea
(Received 29 April 2025; accepted 14 November 2025; published 2 December 2025)
We argue that a discrete bulk spectrum with random statistics appears naturally in the Lorentzian
description of Jackiw-Teitelboim (JT) gravity if an extra confining potential is introduced in the region
where the renormalized geodesic length becomes of order eS0. The existence of such an extra confining
potential may be inferred from the late behavior of complexity and also from the Saad-Shenker-Stanford
(SSS) duality between JT gravity and the matrix model. We derive the explicit form of the extra confining
potential from the well-established density of states obtained in the Euclidean approach to JT gravity. This
extra potential is implicitly determined by the solution of the Abel’s integral equation, which turns out to be
identical to the string equation of the matrix model in the SSS duality formulation of JT gravity. Thanks to
the extra confining potential and the random nature of the spectrum, the time evolution of the Krylov
complexity, which is identified with the renormalized geodesic length, naturally exhibits four phases,
namely, a ramp, a peak, a slope, and a plateau.
DOI: 10.1103/98z9-qdhq
