Non-abelian Ramond-Neveu-Schwarz string theory

We newly construct a world-sheet matrix string theory described by two-dimensional supergravity coupled to supersymmetric Yang-Mills fields where the string coordinates are non-commuting matrices in the gauge group U(N). We show that our string theory has a free string limit where it becomes N-copies of usual Ramond-Neveu-Schwarz strings and can be described by the orbifold conformal field theory being second quantized string theory. In the weak coupling limit, i.e. gs → 0 where gs is the coupling constant of our theory related with the Yang-Mills coupling as gYM-2 = α'gs2, a new additional dimension appears in the string spectrum and it can be speculatively interpreted as the compactified eleven-dimensional coordinate whose dynamics is given by an orbifold O(N) sigma model