Abstract

We will present resolutions of long standing puzzles in supersymmetric gauge
theories. It is well known that the vacuum of super Yang-Mills can be
represented by the Veneziano-Yankielowicz (VY) effective theory. However as
soon as the VY theory was introduced it was understood that it could not be
the whole story. Among the most relevant problems: The VY theory cannot
account for ordinary glueball states and it does not support the expected
domain walls of the underlying theory. We will show that the two puzzles can
be resolved simultaneously. Another important point is that since super Yang-Mills can now be mapped
into one flavor QCD we will be able to export exact results to QCD via the
effective theory and viceversa, i.e. we can use ``experiments'' for QCD to
make predictions for super Yang-Mills. We will probably not have time to discuss new clifford generalizations of
super symmetry which can be interesting for a number of reasons. For example
these are nonanticommuting theories which while lead to noncommuting space
time coordinates they still preserve the Lorentz invariance of the theory.
Besides they might be interesting for lattice simulations, the reason being
that the theories posses only one half of the underlying supersymmetry and
are formulated in the Euclidean space.