Abstract
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 non-commutative tori for arbitrarily close
rational values of Θ. For such values of Θ, 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
Θ, 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 largeN 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 
= 4 super Yang-Mills theory.