Related papers: Matrix Model and Elliptic Curve
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…
A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on the…
We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus…
The framework of emergent gravity arising from Yang-Mills matrix models is developed further, for general noncommutative branes embedded in R^D. The effective metric on the brane turns out to have a universal form reminiscent of the open…
We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with…
These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…
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…
The IKKT or IIB matrix model has been proposed as a non-perturbative definition of type IIB superstring theories. It has the attractive feature that space--time appears dynamically. It is possible that lower dimensional universes dominate…
Matrix models of Yang-Mills type lead to an emergent gravity theory, which may not require fine-tuning of a cosmological constant. We find cosmological solutions of Friedmann-Robertson-Walker type. They generically have a big bounce, and an…
Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding…
We show how gravitational actions, in particular the Einstein-Hilbert action, can be obtained from additional terms in Yang-Mills matrix models. This is consistent with recent results on induced gravitational actions in these matrix models,…
We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with $k=-1$, finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology $a(t) \propto…
We first normalize the derivative Weierstrass $\wp'$-function appearing in Weierstrass equations which give rise to analytic parametrizations of elliptic curves by the Dedekind $\eta$-function. And, by making use of this normalization of…
We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced R-operators…
The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The…
We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric…
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not…
We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a Yang-Mills field, with or without mass term, if the spatial geometry of the underlying spacetime is homothetic to $\R[3]$.…
In this work, we set up the theoretical framework and indicate future applications of symmetric Yang--Mills fields to cosmology. We analyze the coset space dimensional reduction scheme to construct pure Yang--Mills fields on spacetimes…
We investigate the geometry of the matrix model associated with an N=1 super Yang-Mills theory with three adjoint fields, which is a massive deformation of N=4. We study in particular the Riemann surface underlying solutions with arbitrary…