Universality Class of the First Levels in Low-Dimensional Gravity

We investigate the physics of a small group of quantum states defined above the sharply defined ground state of a chaotic ensemble. This "universality class of the first levels" is realized in the majority of "synthetic" random matrix models but, for all we know, in only one microscopically defined system: low-dimensional gravity. We discuss the physical properties of these states, notably their exceptional rigidity against external perturbations, as quantified by the so-called quantum state fidelity. Examining these structures through the lenses of random matrix and string theory, we highlight their relevance to the physics of low-dimensional holographic principles.