In this thesis, we study one-dimensional, matrix-valued quantum mechanical models. These
models, exhibit numerous characteristics and can be used to study various problems. One …

Matrix models, as quantum mechanical systems without explicit spatial dependence, provide
valuable insights into higher-dimensional gauge and gravitational theories, especially within …

A bstract We take a step towards the non-perturbative description of a two-dimensional
dilaton-gravity theory which has a vanishing cosmological constant and contains black …

Matrix quantum mechanics plays various important roles in theoretical physics, such as a
holographic description of quantum black holes, and it underpins the only practical …

Inspired by the program of discrete holography, we show that Jackiw-Teitelboim (JT) gravity
on a hyperbolic tiling of Euclidean AdS $ _2 $ gives rise to an Ising model on the dual lattice …

A bstract Matrix models play an important role in studies of quantum gravity, being
candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we …

This contribution is not intended as a review but, by suggestion of the editors, as a glimpse
ahead into the realm of dually weighted tensor models for quantum gravity. This class of …

Large N matrix quantum mechanics is central to holographic duality but not solvable in the
most interesting cases. We show that the spectrum and simple expectation values in these …

In the context of holographic dualities [1], one can use a non-gravitational theory–typically a
Yang-Mills theory of rank N and effective coupling R, to describe gravitational dynamics in a …

A bstract We propose a local renormalization group procedure where length scale is
changed in spacetime dependent way. Combining this scheme with an earlier observation …