Related papers: Notes on Matrix Models
We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known…
We propose a novel method of finding the classical limit of the matrix geometry. We define coherent states for a general matrix geometry described by a large-N sequence of D Hermitian matrices X_\mu (\mu =1,2, ..., D) and construct a…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
These lecture notes give a pedagogical and (mostly) self-contained review of some basic aspects of the Matrix model of M-theory. The derivations of the model as a regularized supermembrane theory and as the discrete light-cone quantization…
Matrix models of Yang-Mills type induce an effective gravity theory on 4-dimensional branes, which are considered as models for dynamical space-time. We review recent progress in the understanding of this emergent gravity. The metric is not…
In this survey article, we describe recent work that connects three separate objects of interest: totally nonnegative matrices; quantum matrices; and matrix Poisson varieties.
This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of…
In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations,…
Rectangular $N\times M$ matrix models can be solved in several qualitatively distinct large $N$ limits, since two independent parameters govern the size of the matrix. Regarded as models of random surfaces, these matrix models interpolate…
A class of background independent matrix models is made for which the structure of both local gauge symmetries and classical solutions is clarified. These matrix models do not involve a space-time metric and provide the matrix analogs of…
This paper is a collection of lecture notes on modified gravity. Various modified gravity models formulated within the Riemannian formalism are discussed.
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
A self-contained review is given of the matrix model of M-theory. The introductory part of the review is intended to be accessible to the general reader. M-theory is an eleven-dimensional quantum theory of gravity which is believed to…
We summarize some (mostly geometric) facts underlying the relation between 2D integrable sigma models and generalized Gross-Neveu models, emphasizing connections to the theory of nilpotent orbits, Springer resolutions and quiver varieties.…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…