Related papers: Matrix models of 2d gravity
General matterless models of gravity include dilaton gravity, arbitrary powers in curvature, but also dynamical torsion. They are a special class of "Poisson-sigma-models" whose solutions are known completely, together with their general…
Recent results on the annulus partition function in Liouville field theory are applied to non-critical string theory, both below and above the critical dimension. Liouville gravity coupled to $c\le 1$ matter has a dual formulation as a…
These lectures present some topics of string phenomenology and contain two parts. In the first part, I review the possibility of lowering the string scale in the TeV region, that provides a theoretical framework for solving the mass…
This paper is a collection of lecture notes on modified gravity. Various modified gravity models formulated within the Riemannian formalism are discussed.
Following is a collection of lecture notes on D-branes, which may be used by the reader as preparation for applications to modern research applications such as: the AdS/CFT and other gauge theory/geometry correspondences, Matrix Theory and…
This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since…
We formulate matrix string models on a class of exact string backgrounds with non constant RR-flux parameterized by a holomorphic prepotential function and with manifest (2,2) supersymmetry. This lifts these string theories to M-theory…
Beginning with a review of the arguments leading to the so-called c=1 barrier in the continuum formulation of noncritical string theory, the pathology is then exhibited in a discretized version of the theory, formulated through dynamical…
Some of the recent developments in the theory of random surfaces and simplicial quantum gravity is reviewed. For 2d quantum gravity this includes the failure of Regge calculus, our improved understanding of the $c>1$ regime, some surprises…
The study of the so called brane world models has introduced completely new ways of looking up on standard problems in many areas of theoretical physics. Inspired in the recent developments of string theory, the Brane World picture involves…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…
The foundations of matrix geometry are discussed, which provides the basis for recent progress on the effective geometry and gravity in Yang-Mills matrix models. Basic examples lead to a notion of embedded noncommutative spaces (branes)…
General properties of a class of two-dimensional dilaton gravity (DG) theories with multi-exponential potentials are studied and a subclass of these theories, in which the equations of motion reduce to Toda and Liouville equations, is…
Ideas recently put forward by Y. Matsuo and the author are summarized on the example of the simplest ($W_3$) generalization of two-dimensional gravity. These notes are based on lectures given at the workshop `` Strings, Conformal Models and…
In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results…
We introduce {\it conformal multi-matrix models} (CMM) as an alternative to conventional multi-matrix model description of two-dimensional gravity interacting with $c < 1$ matter. We define CMM as solutions to (discrete) extended Virasoro…
Large-N matrix models coupled via multitrace operators are used to define, via appropriate double-scaling limits, solvable models of interacting multi-string theories. It is shown that although such theories are non-local at the world-sheet…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…