  A consistent formulation of a fully supersymmetric theory on the lattice has
been a long standing challenge. In recent years there has been a renewed
interest on this problem with different approaches. At the basis of the
formulation we present in the following there is the Dirac-Kahler twisting
procedure, which was proposed in the continuum for a number of theories,
including N=4 SUSY in four dimensions. Following the formalism developed in
recent papers, an exact supersymmetric theory with two supercharges on a one
dimensional lattice is realized using a matrix-based model. The matrix
structure is obtained from the shift and clock matrices used in two dimensional
non-commutative field theories. The matrix structure reproduces on a one
dimensional lattice the expected modified Leibniz rule. Recent claims of
inconsistency of the formalism are discussed and shown not to be relevant.

High Energy Physics - Lattice