  The SO(32) theory, in the limit where it is an open superstring theory, is
completely specified in the light-cone gauge as a second-quantized string
theory in terms of a ``matrix string'' model. The theory is defined by the
neighbourhood of a 1+1 dimensional fixed point theory, characterized by an
Abelian gauge theory with type IB Green-Schwarz form. Non-orientability and
SO(32) gauge symmetry arise naturally, and the theory effectively constructs an
orientifold projection of the (weakly coupled) matrix type IIB theory (also
discussed herein). The fixed point theory is a conformal field theory with
boundary, defining the free string theory. Interactions involving the interior
of open and closed strings are governed by a twist operator in the bulk, while
string end-points are created and destroyed by a boundary twist operator.
