Supersymmetric Field Theories on Noncommutative Spaces

Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its representation. As a result, we will see that the action has a close relationship with IIB matrix model

Gauge Theory and a Dirac Operator on a Noncommutative Space

As a tool to carry out the quantization of gauge theory on a noncommutative space, we present a Dirac operator that behaves as a line element of the canonical noncommutative space. Utilizing this operator, we construct the Dixmier trace, which is the regularized trace for infinite-dimensional matrices. We propose the possibility of solving the cosmological constant problem by applying our gauge theory on the noncommutative space.Comment: 2 figures, final versio

Unitary-Matrix Integration on 2D Yang-Mills Action

Using the idea of Itzykson-Zuber integral, unitary-matrix integration of 2D Yang-Mills action is presented. The uniqueness of the solution of heat equation enables us to integrate out the unitary-matrix parts of hermite matrices and to obtain the expression of integration over vectors, also in this case.Comment: 8 page

Nucleon Decay Matrix Elements from Lattice QCD

We present a GUT-model-independent calculation of hadron matrix elements for all dimension-six operators associated with baryon number violating processes using lattice QCD. Our results cover all the matrix elements required to estimate the partial lifetimes of (proton,neutron)$\to$($\pi,K,\eta$) +(${\bar \nu},e^+,\mu^+$) decay modes. We point out the necessity of disentangling two form factors that contribute to the matrix elements; previous calculations did not make the separation, which led to an underestimate of the physical matrix elements. With a correct separation, we find that the matrix elements have values 3-5 times larger than the smallest estimates employed in phenomenological analyses of the nucleon decays, which gives stronger constraints on GUT models. We also find that the values of the matrix elements are comparable with the tree-level predictions of chiral Lagrangian.Comment: 10 pages, 3 figures as eps-file. Invited talk at 2nd Workshop on Neutrino Oscillations and Their Origin (NOON 2000), Tokyo, Japan, 6-18 Dec 200

Lattice QCD Calculation of Flavor Singlet Matrix Elements and N-N Scattering Lengths

We report on our recent study of flavor singlet matrix elements calculated with the wall source method without gauge fixing. Results are presented for the mass difference between $\eta^{\prime}$ and pseudoscalar octet mesons, the $\pi$-N $\sigma$ term and the proton axial vector matrix elements. An exploratory calculation of the N-N scattering lengths is also discussed including a phenomenological study with one-boson exchange potentials.Comment: 12 pages, latex source-file, 5 figures as epsf-file, talk presented at ''QCD on massively parallel computers'' (Yamagata, Japan, March 16-18 1995