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

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.

Scalar Solitons on the Fuzzy Sphere

We study scalar solitons on the fuzzy sphere at arbitrary radius and noncommutativity. We prove that no solitons exist if the radius is below a certain value. Solitons do exist for radii above a critical value which depends on the noncommutativity parameter. We construct a family of soliton solutions which are stable and which converge to solitons on the Moyal plane in an appropriate limit. These solutions are rotationally symmetric about an axis and have no allowed deformations. Solitons that describe multiple lumps on the fuzzy sphere can also be constructed but they are not stable.Comment: 24 pages, 2 figures, typo corrected and stylistic changes. v3: reference adde

Spin-Blockade in Single and Double Quantum Dots in Magnetic Fields: a Correlation Effect

The total spin of correlated electrons in a quantum dot changes with magnetic field and this effect is generally linked to the change in the total angular momentum from one magic number to another, which can be understood in terms of an `electron molecule' picture for strong fields. Here we propose to exploit this fact to realize a spin blockade, i.e., electrons are prohibited to tunnel at specific values of the magnetic field. The spin-blockade regions have been obtained by calculating both the ground and excited states. In double dots the spin-blockade condition is found to be less stringent than in single dots.Comment: 4pages, to be published in Phys. Rev. B (Rapid Communication

Vertically coupled double quantum dots in magnetic fields

Ground-state and excited-state properties of vertically coupled double quantum dots are studied by exact diagonalization. Magic-number total angular momenta that minimize the total energy are found to reflect a crossover between electron configurations dominated by intra-layer correlation and ones dominated by inter-layer correlation. The position of the crossover is governed by the strength of the inter-layer electron tunneling and magnetic field. The magic numbers should have an observable effect on the far infra-red optical absorption spectrum, since Kohn's theorem does not hold when the confinement potential is different for two dots. This is indeed confirmed here from a numerical calculation that includes Landau level mixing. Our results take full account of the effect of spin degrees of freedom. A key feature is that the total spin, $S$, of the system and the magic-number angular momentum are intimately linked because of strong electron correlation. Thus $S$ jumps hand in hand with the total angular momentum as the magnetic field is varied. One important consequence of this is that the spin blockade (an inhibition of single-electron tunneling) should occur in some magnetic field regions because of a spin selection rule. Owing to the flexibility arising from the presence of both intra-layer and inter-layer correlations, the spin blockade is easier to realize in double dots than in single dots.Comment: to be published in Phys. Rev. B1

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