  We study aspects of gauge theory on tori which are a consequences of Morita
equivalence. In particular we study the behavior of gauge theory on
noncommutative tori for arbitrarily close rational values of Theta. For such
values of Theta, there are Morita equivalent descriptions in terms of
Yang-Mills theories on commutative tori with very different magnetic fluxes and
rank. In order for the correlators of open Wilson lines to depend smoothly on
Theta, the correlators of closed Wilson lines in the commutative Yang-Mills
theory must satisfy strong constraints. If exactly satisfied, these constraints
give relations between small and large N gauge theories. We verify that these
constraints are obeyed at leading order in the 1/N expansion of pure 2-d QCD
and of strongly coupled N=4 super Yang-Mills theory.
