Representation of SU(infinity) Algebra for Matrix Models

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N^2-1) times (N^2-1) matrices of the SU(N) generators go to those of the Poisson algebra in the large N limit. However, it is not the case for the N times N matrices in the fundamental representation.Comment: 8 page

Polyakov Lines in Yang-Mills Matrix Models

We study the Polyakov line in Yang-Mills matrix models, which include the IKKT model of IIB string theory. For the gauge group SU(2) we give the exact formulae in the form of integral representations which are convenient for finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper bounds which decay as a power law at large momentum p. We argue that these capture the full asymptotic behaviour. We also indicate how to extend the results to some correlation functions of Polyakov lines.Comment: 19 pages, v2 typos corrected, v3 ref adde

Matrix Models

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 of Yang--Mills model respectively. They are obtained via the deformations of string/membrane worldsheet/worldvolume. Classical solutions leading to noncommutative gauge models are considered.Comment: Lectures given at the Winter School on Modern Trends in Supersymmetric Mechanics, March 2005 Frascati; 38p

Effect of Interaction on the Formation of Memories in Paste

A densely packed colloidal suspension with plasticity, called paste, is known to remember directions of vibration and flow. These memories in paste can be visualized by the morphology of desiccation crack patterns. Here, we find that paste made of charged colloidal particles cannot remember flow direction. If we add sodium chloride into such paste to screen the Coulombic repulsive interaction between particles, the paste comes to remember flow direction. That is, one drop of salt water changes memory effect in the paste and thereby we can tune the morphology of desiccation crack patterns more precisely.Comment: 10 pages, 11 figures, Title change

Axial anomaly in the reduced model: Higher representations

The axial anomaly arising from the fermion sector of \U(N) or \SU(N) reduced model is studied under a certain restriction of gauge field configurations (the ``\U(1) embedding'' with $N=L^d$). We use the overlap-Dirac operator and consider how the anomaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of $L^2$ (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general gauge-group representations in the large $N$ limit. The large $N$ limit exhibits expected algebraic properties as the axial anomaly. Nevertheless, when the gauge group is \SU(N), it does not have a structure such as the trace of a product of traceless gauge-group generators which is expected from the corresponding gauge field theory.Comment: 21 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHE