Matrix description of intersecting M5 branes

Novel 3+1 dimensional N = 2 superconformal field theories (with tensionless BPS string solitons) are believed to arise when two sets of M5 branes inte rsect over a 3+1 dimensional hyperplane. We derive a DLCQ description of th ese theories as supersymmetric quantum mechanics on the Higgs branch of sui table 4d N = 1 supersymmetric gauge theories. Our formulation allows us to determine the scaling dimensions of certain chiral primary operators in the conformal field theories. We also discuss general criteria for quantum mec hanical DLCQ descriptions of supersymmetric field theories (and the resulti ng multiplicities and scaling dimensions of chiral primary operators).