We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the
gauge where the field strength is diagonal. Twisted sectors originate, as in
Matrix string theory, from permutations of the eigenvalues around homotopically
non-trivial loops. These sectors, that must be discarded in the usual
quantization due to divergences occurring when two eigenvalues coincide, can be
consistently kept if one modifies the action by introducing a coupling of the
field strength to the space-time curvature. This leads to a generalized
Yang-Mills theory whose action reduces to the usual one in the limit of zero
curvature. After integrating over the non-diagonal components of the gauge
fields, the theory becomes a free string theory (sum over unbranched coverings)
with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to
a lattice theory with a gauge group which is the semi-direct product of S_N and
U(1)^N. By using well known results on the statistics of coverings, the
partition function on arbitrary Riemann surfaces and the kernel functions on
surfaces with boundaries are calculated. Extensions to include branch points
and non-abelian groups on the world-sheet are briefly commented upon.Comment: Latex2e, 29 pages, 2 .eps figure
