M theory, Joyce Orbifolds and Super Yang-Mills

We geometrically engineer d=4 N=1 supersymmetric Yang-Mills theories by considering M theory on various Joyce orbifolds. We argue that the superpotential of these models is generated by fractional membrane instantons. The relation of this superpotential to membrane anomalies is also discussed.Comment: v2: A careless error which appeared at the end of section four and propagated to section six has been corrected. (The mistake was to identify the Coxeter number of the gauge group with the order of a certain finite group). The results are unchanged. Some references have also been added. v3: A previously unrecognised monodromy recognised. New monodromy free examples added. 21 pages, Late

N=1 Heterotic/M-theory Duality and Joyce Manifolds

We present an ansatz which enables us to construct heterotic/M-theory dual pairs in four dimensions. It is checked that this ansatz reproduces previous results and that the massless spectra of the proposed dual pairs agree. The new dual pairs consist of M-theory compactifications on Joyce manifolds of $G_2$ holonomy and Calabi-Yau compactifications of heterotic strings. These results are further evidence that M-theory is consistent on orbifolds. Finally, we interpret these results in terms of M-theory geometries which are K3 fibrations and heterotic geometries which are conjectured to be $T^3$ fibrations. Even though the new dual pairs are constructed as non-freely acting orbifolds of existing dual pairs, the adiabatic argument is apparently not violated.Comment: 25 pages, Late

Multimuons events and primary composition

Nucleon decay detectors at large depths offers now a total area larger than 1000 sq m to registrate muons of energy exceeding 1 TeV. Near complete high energy muon families are detected in those arrays. An extensive 3D Monte-Carlo simulation was conducted in view to understand the spatial distribution of those events and the possible link with elementary act or primary composition. As pion or kaon parents have a very small decay probability at so high energy, multimuon phenomena occurs at high altitude where the atmospheric density is small after the most energetic collisions