Constructing the superstring space-time SUSY algebra in the light-cone gauge

Closure of the [10] SUSY algebra is attempted for heterotic and type II superstrings by explicit constructions of the quartic supersymmetry and Hamiltonian generators. These are shown to possess only contact interactions. Other related nonlinearly realized generators are also constructed at the quartic level, and a substantial part of the [10]-SUSY algebra shown to close with only these generators, for any regularization scheme for the heterotic, and by using phase integration for the type II. Type I superstrings are also considered