Related papers: Notes on Matrix Models
An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2x2) matrices. The method is based on the measurement of…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
Matrix models and their connections to String Theory and noncommutative geometry are discussed. Various types of matrix models are reviewed. Most of interest are IKKT and BFSS models. They are introduced as 0+0 and 1+0 dimensional reduction…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
This paper discusses the somewhat unintuitive conjecture that many Lorentz-invariant many-particle models can be reinterpreted to satisfy the gtr field equations. It is shown that a careful remapping of coordinates yields a non-trivial…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
A brief review of the eigenvalue matrix model integrability and superintegrability properties, focused on the simplest, still representative, Gaussian Hermitian case.
This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The…
We extend the formalism of Hamiltonian string bit models of quantum gravity type in two spacetime dimensions to include couplings to particles. We find that the single-particle closed and open universe models respectively behave like empty…
In the first part of the talk, I review the applications of loop equations to the matrix models and to 2-dimensional quantum gravity which is defined as their continuum limit. The results concerning multi-loop correlators for low genera and…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
Motivated by the formalism of string bit models, or quantum matrix models, we study a class of simple Hamiltonian models of quantum gravity type in two space-time dimensions. These string bit models are special cases of a more abstract…
We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…
We consider the insertion of integrable boundaries for a class of supersymmetric quantum models. The generic conditions for constructing purely bosonic, purely fermionic or mixed type solutions of the graded reflection equation are…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
We review experiments and theoretical models about the possible mutual interplay between the gravitational field and materials in the superconducting state or other macroscopic quantum states. More generally, we focus on the possibility for…