A New Model of Direct Gauge Mediation with an Affine Quantum Moduli Space

We present a new, simple supersymmetry breaking model with direct gauge mediation. Supersymmetry breaking sector is based on the model with an Affine quantum moduli space. The model has no gauge messengers and no light scalars charged under the Standard Model which give a negative contribution to the soft masses. Large expectation value at the minimum is obtained by balancing the runaway potential and the dimension six nonrenormalizable term. This makes it easy to preserve the perturbative unification. Enough suppression of the supergravity contribution to the soft masses can also be shown.Comment: 8 pages, LaTeX, the version to appear in Physics Letters

More on N=1 Self-Dualities and Exceptional Gauge Groups

Starting from a generalization of a recent result on self-duality we systematically analyze self-dual models. We find a criterion to judge whether a given model is self-dual or not. With this tool we construct some new self-dual pairs, focussing on examples with exceptional gauge groups.Comment: 10 pages, LaTeX2e, using utarticle.cls (included

Some results and problems for anisotropic random walks on the plane

This is an expository paper on the asymptotic results concerning path behaviour of the anisotropic random walk on the two-dimensional square lattice Z^2. In recent years Mikl\'os and the authors of the present paper investigated the properties of this random walk concerning strong approximations, local times and range. We give a survey of these results together with some further problems.Comment: 20 page

Exact Results in SO(11) SUSY Gauge Theories with Spinor and Vector Matter

We investigate the confining phase vacuum structure of supersymmetric SO(11) gauge theories with one spinor matter field and Nf \le 6 vectors. We describe several useful tricks and tools that facilitate the analysis of these chiral models and many other theories of similar type. The forms of the Nf=5 and Nf=6 quantum moduli spaces are deduced by requiring that they reproduce known results for SU(5) SUSY QCD along the spinor flat direction. After adding mass terms for vector fields and integrating out heavy degrees of freedom, we also determine the dynamically generated superpotentials in the Nf \le 4 quantum theories. We close with some remarks regarding magnetic duals to the Nf \ge 7 electric SO(11) theories.Comment: 16 pages, harvmac and tables macro