We consider two-dimensional Yang-Mills theories on arbitrary Riemann
surfaces. We introduce a generalized Yang-Mills action, which coincides with
the ordinary one on flat surfaces but differs from it in its coupling to
two-dimensional gravity. The quantization of this theory in the unitary gauge
can be consistently performed taking into account all the topological sectors
arising from the gauge-fixing procedure. The resulting theory is naturally
interpreted as a Matrix String Theory, that is as a theory of covering maps
from a two-dimensional world-sheet to the target Riemann surface.Comment: LaTeX, 10 pages, uses espcrc2.sty. Presented by A. D'adda at the
Third Meeting on Constrained Dynamics and Quantum Gravity, Villasimius
(Sardinia, Italy) September 13-17, 1999; to appear in the proceeding