Non commutative geometry and super Yang-Mills theory

We aim to connect the non commutative geometry ``quotient space'' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory. This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size \Sigma / N with the boundary conditions given by a system with p units of magnetic flux. The transition to irrational parameter can be obtained by letting N and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification.Comment: 11 pages, LaTeX, two .gif files of (hand sketched) figures; a misprint corrected and some references adde

Ground State Structure of a Coupled 2-Fermion System in Supersymmetric Quantum Mechanics

We prove the uniqueness of the ground state for a supersymmetric quantum mechanical system of two fermions and two bosons, which is closely related to the N=1 WZ-model. The proof is constructive and gives detailed information on what the ground state looks like.Comment: 8 pages, LaTe

Finite-Time Amplitudes In Matrix Theory

We evaluate one-loop finite-time amplitudes for graviton scattering in Matrix theory and compare to the corresponding amplitudes in supergravity. We find agreement for arbitrary time intervals at leading order in distance, providing a functional agreement between supergravity and Matrix theory. At subleading order, we find corrections to the effective potential found from previous phase shift calculations in Matrix theory.Comment: 12 pages, harvmac, reference added, typo correcte

Bound states and resonances in the scalar sector of the MSSM

The trilinear couplings of squarks and sleptons to the Higgs bosons can give rise to a spectrum of bound states with exotic quantum numbers, for example, those of a leptoquark.Comment: 8 pages, 2 eps figures, latex, epsf; published version (minor changes in wording and referencing

Nucleon Decay Matrix Elements for Domain-Wall Fermions

We report on the nucleon decay matrix elements with domain-wall fermions in quenched approximation. Results from direct and indirect method are compared with a focus on the process of a proton decaying to a pion and a lepton. We discuss the renormalization necessary for the matching to the continuum theory. Preliminary results for the renormalized chiral lagrangian parameters are presented.Comment: Lattice2002(matrixel), 3 pages, 1 figur

Tales of D0 on D6 Branes: Matrix Mechanics of Identical Particles

We investigate a class of matrix model which describes the dynamics of identical particles in even dimentional space. We show that the degrees of freedom after some constraints are implimented is proportional to particle number and consist of those for positions and internal degrees. The particle dynamics is given by the metric on the smooth moduli space. The moduli space metric for two particles is found. The size of tightly packed $N$ particles grows like $\sqrt{N}$. Our matrix model is related to the matrix model for fractional quantum Hall effect, the ADHM formalism of U(1) instantons on noncommutative space, and supersymmetric D0 branes on D6 branes with nonzero B-field in type IIA theory.Comment: a latex file, 11 page, no figur

Towards the lattice study of M-theory (II)

We present new results of the quenched simulations of the reduced D=4 supersymmetric Yang - Mills quantum mechanics for larger gauge groups SU(N), 2<N<9. The model, studied at finite temperature, reveals existence of the two distinct regions which may be precursors of a black hole and the elementary D0 branes phases of M-theory conjectured in the literature. Present results for higher groups confirm the picture found already for N=2. Similar behaviour is observed in the preliminary simulations for the D=6 and D=10 models.Comment: Talk presented at XIX International Symposium on Lattice Field Theory lattice2001(surfaces

Creation of Strings in D-particle Quantum Mechanics

D-particle quantum mechanics in a type I' background is reviewed. It is also discussed how a string is created when a D-particle is taken through a D8-brane. The process is found to be dual to the creation of a D3-brane when a NS5 and D5 brane are passed through each other.Comment: 6 pages, 2 figures. Uses espcrc2.sty. Talk given at STRINGS'9