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 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

Gate Adjustable Coherent Three and Four Level Mixing in a Vertical Quantum Dot Molecule

We study level mixing in the single particle energy spectrum of one of the constituent quantum dots in a vertical double quantum dot by performing magneto-resonant-tunneling spectroscopy. The device used in this study differs from previous vertical double quantum dot devices in that the single side gate is now split into four separate gates. Because of the presence of natural perturbations caused by anharmonicity and anistrophy, applying different combinations of voltages to these gates allows us to alter the effective potential landscape of the two dots and hence influence the level mixing. We present here preliminary results from one three level crossing and one four level crossings high up in the energy spectrum of one of the probed quantum dots, and demonstrate that we are able to change significantly the energy dispersions with magnetic field in the vicinity of the crossing regions.Comment: 5 pages, 4 figures. MSS-14 conference proceedings submitted to Physica

The Cohomological Supercharge

We discuss the supersymmetry operator in the cohomological formulation of dimensionally reduced SYM. By establishing the cohomology, a large class of invariants are classified.Comment: 12 pages, latex, no figures. Typo corrected in eqn 3.

Adding a Myers Term to the IIB Matrix Model

We show that Yang-Mills matrix integrals remain convergent when a Myers term is added, and stay in the same topological class as the original model. It is possible to add a supersymmetric Myers term and this leaves the partition function invariant.Comment: 8 pages, v2 2 refs adde

On the Quantum Geometry of String Theory

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 the theory, therefore providing a dynamical solution to the reduction of space--time dimensionality. We summarize recent works that show the central role of the phase of the fermion determinant in the possible realization of such a scenario.Comment: 3 pages, 2 figures, Lattice2001(surfaces

Yang-Mills Matrix Theory

We discuss bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. We begin by finding convergence conditions for the partition and correlation functions. Moving on, we specialise to the SU(N) models with large N. In both the Yang-Mills and cohomological formulations, we find all quantities which are invariant under the supercharges. Finally, we apply the deformation method of Moore, Nekrasov and Shatashvili directly to the Yang-Mills model. We find a deformation of the action which generates mass terms for all the matrix fields whilst preserving some supersymmetry. This allows us to rigorously integrate over a BRST quartet and arrive at the well known formula of MNS.Comment: PhD thesis, 78 pages, reference adde

Bosonization approach to the edge reconstruction of two dimentional electron systems in a quantum dot

We consider the edge reconstruction of electrons in a two dimensional harmonic trap under a strong magnetic field. In this system the edge reconstruction occurs as a result of competition between electron-electron interaction and confining potential. To describe it, we develop a bosonization scheme for two dimensional electron systems. With this method we obtain the excitation spectrum and demonstrate that the edge reconstruction occurs when the value of the magnetic field reaches a critical value. We also show that the edge reconstruction depends on the number of electrons. Additionally, we calculate the third order terms of bosons in Hamiltonian and examine the effect of those terms with a perturbation theory.Comment: 5pages, 6figure

Two level anti-crossings high up in the single-particle energy spectrum of a quantum dot

We study the evolution with magnetic field of the single-particle energy levels high up in the energy spectrum of one dot as probed by the ground state of the adjacent dot in a weakly coupled vertical quantum dot molecule. We find that the observed spectrum is generally well accounted for by the calculated spectrum for a two-dimensional elliptical parabolic confining potential, except in several regions where two or more single-particle levels approach each other. We focus on two two-level crossing regions which show unexpected anti-crossing behavior and contrasting current dependences. Within a simple coherent level mixing picture, we can model the current carried through the coupled states of the probed dot provided the intrinsic variation with magnetic field of the current through the states (as if they were uncoupled) is accounted for by an appropriate interpolation scheme.Comment: 4 pages, 4 figures, accepted for publication in Physica E in MSS 13 conference proceeding