Lattice supersymmetry in 1D with two supercharges

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 ap-proaches. At the basis of the formulation we present in the following there is the Dirac-Kähler 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 ex-act 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. The XXV International Symposium on Lattice Field Theor