Dongsu Bak

A bstract: In Jackiw-Teitelboim gravity, the naive Schwarzian quantum mechanics leads to a continuous bulk spectrum, in apparent contradiction with the finite entropy of the black hole, which requires a discrete spectrum with level spacing of order e ^{− S 0} . It was recently shown that restoring spectral discreteness with random statistics requires the introduction of a left confining potential that becomes relevant when the renormalized wormhole length reaches order e ^{S 0} . In this work, we show how the known perturbative results of JT gravity are recovered within this modified framework. More importantly, we demonstrate that this modification has a direct dynamical consequence: it resolves the black-hole singularity. The confining potential generates a repulsive force at exponentially large wormhole length, preventing the indefinite growth that would otherwise lead to a singularity. We explain in detail how this turnaround arises and explore its implications for late-time bulk gravitational dynamics, the disappearance of horizons, and possible observational consequences.

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 e S 0 . 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.

Traditional weak-lensing mass reconstruction techniques suffer from various artifacts, including noise amplification and the mass-sheet degeneracy. In S. E. Hong et al., we demonstrated that many of these pitfalls of traditional mass reconstruction can be mitigated using a deep learning approach based on a convolutional neural network (CNN). In this paper, we present our improvements and report on the detailed performance of our CNN algorithm applied to next-generation wide-field (WF) observations. Assuming the field of view ( 3 . ° 5 × 3 . ° 5 ) and depth (27 mag at 5σ) of the Vera C. Rubin Observatory, we generated training data sets of mock shear catalogs with a source density of 33 arcmin⁻² from cosmological simulation ray-tracing data. We find that the current CNN method provides high-fidelity reconstructions consistent with the true convergence field, restoring both small- and large-scale structures. In addition, the cluster detection utilizing our CNN reconstruction achieves ∼75% completeness down to ∼10¹⁴ M _⊙. We anticipate that this CNN-based mass reconstruction will be a powerful tool in the Rubin era, enabling fast and robust WF mass reconstructions on a routine basis.

We show that the (1,0) tensor and hypermultiplet supersymmetry variations can be uplifted to loop space. Upon dimensional reduction we make contact with abelian five-dimensional super Yang-Mills, which has a nonabelian generalization that we subsequently uplift back to loop space where we conjecture a nonabelian generalization of the (1,0) supersymmetry variations and demonstrate their on-shell closure.

We study canonical quantization of Jackiw-Teibelboim (JT) gravity coupled to a massless scalar field. We provide concrete expressions of matter SL(2,{\,\bf R}) charges and the boundary matter operators in terms of the creation and annihilation operators in the scalar field. The matter charges are represented in the form of an oscillator (Jordon-Schwinger) realization of the SL(2,{\,\bf R}) algebra. We also show how the gauge constraints are implemented classically, by matching explicitly classical solutions of Schwarzian dynamics with bulk solutions. We introduce $n$-point transition functions defined by insertions of boundary matter operators along the two-sided Lorentzian evolution, which may fully spell out the quantum dynamics in the presence of matter. For the Euclidean case, we proceed with a two-sided picture of the disk geometry and consider the two-sided $2$-point correlation function where initial and final states are arranged by inserting matter operators in a specific way. For some simple initial states, we evaluate the correlation function perturbatively. We also discuss some basic features of the two-sided correlation functions with additional insertions of boundary matter operators along the two-sided evolution.