  Non-commutative gauge theory with a non-constant non-commutativity parameter
can be formulated as a decoupling limit of open strings ending on D3-branes
wrapping a Melvin universe. We construct the action explicitly and discuss
various physical features of this theory. The decoupled field theory is not
supersymmetric. Nonetheless, the Coulomb branch appears to remain flat at least
in the large N and large 't Hooft coupling limit. We also find the analogue of
Prasad-Sommerfield monopoles whose size scales with the non-commutativity
parameter and is therefore position dependent.
