Supersymmetric Yang-Mills Theories on the Lattice: Part I - Construction

Certain classes of supersymmetric Yang-Mills (SYM) theories including the well known N=4 SYM, that takes part in the AdS/CFT correspondence, can be formulated on the lattice using the techniques of exact lattice supersymmetry. In this talk I will provide the construction of such theories and describe how great ideas such as topological field theories, Dirac-Kahler fermions, geometric discretization all come together to create lattice SYM theories that are exact-supersymmetric, gauge-invariant and doubler-free on the lattice.