Convergent Yang-Mills Matrix Theories

We consider the partition function and correlation functions in the bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. In the supersymmetric case, we show that the partition function converges when $D=4,6$ and 10, and that correlation functions of degree $k< k_c=2(D-3)$ are convergent independently of the group. In the bosonic case we show that the partition function is convergent when $D \geq D_c$, and that correlation functions of degree $k < k_c$ are convergent, and calculate $D_c$ and $k_c$ for each group, thus extending our previous results for SU(N). As a special case these results establish that the partition function and a set of correlation functions in the IKKT IIB string matrix model are convergent.Comment: 21 pages, no figures, JHEP style, typos corrected, 1 reference adde

The spectral dimension of the branched polymers phase of two-dimensional quantum gravity

The metric of two-dimensional quantum gravity interacting with conformal matter is believed to collapse to a branched polymer metric when the central charge c>1. We show analytically that the spectral dimension of such a branched polymer phase is four thirds. This is in good agreement with numerical simulations for large c.Comment: 29 pages plain LateX2e, 7 eps figures included using eps

Avalanche size distribution in a random walk model

We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches and other self-organized critical phenomena in one dimension. We find scaling laws relating the frequency, size and width of avalanches and an exponent $4/3$ in the size distribution law.Comment: 16 pages Latex, macros included, 3 postscript figure

The phase diagram of an Ising model on a polymerized random surface

We construct a random surface model with a string susceptibility exponent one quarter by taking an Ising model on a random surface and introducing an additional degree of freedom which amounts to allowing certain outgrowths on the surfaces. Fine tuning the Ising temperature and the weight factor for outgrowths we find a triple point where the susceptibility exponent is one quarter. At this point magnetized and nonmagnetized gravity phases meet a branched polymer phase.Comment: Latex file, 10 pages, macros included. Two EPS figure

The Convergence of Yang-Mills Integrals

We prove that SU(N) bosonic Yang-Mills matrix integrals are convergent for dimension (number of matrices) $D\ge D_c$. It is already known that $D_c=5$ for N=2; we prove that $D_c=4$ for N=3 and that $D_c=3$ for $N\ge 4$. These results are consistent with the numerical evaluations of the integrals by Krauth and Staudacher.Comment: 13 pages, no figures, uses JHEP class. Extra references adde

Symmetries in QFT

This document contains notes from the graduate lecture course, "Symmetries in QFT" given by J.F.Wheater at Oxford University in Hilary term. The course gives an informal introduction to QFT.Comment: Lecture note

The Spectral Dimension of Non-generic Branched Polymer Ensembles

We show that the spectral dimension on non-generic branched polymer models with susceptibility exponent $\gamma$ is given by $2/(1+\gamma)$. For those models with negative $\gamma$ we find that the spectral dimension is 2.Comment: 10 pages plain LateX2e, 1 eps figures included using eps

Bottleneck Surfaces and Worldsheet Geometry of Higher-Curvature Quantum Gravity

We describe a simple lattice model of higher-curvature quantum gravity in two dimensions and study the phase structure of the theory as a function of the curvature coupling. It is shown that the ensemble of flat graphs is entropically unstable to the formation of baby universes. In these simplified models the growth in graphs exhibits a branched polymer behaviour in the phase directly before the flattening transition.Comment: 18 pages LaTeX, 3 .eps figures, uses epsf.tex; clarifying comments added and typos correcte

The spectral dimension of non-generic branched polymers

We show that the spectral dimension on non-generic branched polymers with positive susceptibility exponent is given by $d_s=2/(1+\gamma)$. For those models with $\gamma<0$ we find that $d_s=2$.Comment: LATTICE98(surfaces

Three-Dimensional Quantum Gravity Coupled to Gauge Fields

We show how to simulate U(1) gauge fields coupled to three-dimensional quantum gravity and then examine the phase diagram of this system. Quenched mean field theory suggests that a transition separates confined and deconfined phases (for the gauge matter) in both the negative curvature phase and the positive curvature phase of the quantum gravity, but numerical simulations find no evidence for such transitions.Comment: 16 page