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We study supergravity solutions of type II branes wrapping a Melvin universe. These solutions
provide the gravity description of non-commutative field theories with non-constant non-commutativity
parameter. Typically these theories are non-supersymmetric, though they exhibit some feature
of their corresponding supersymmetric theories.
An interesting feature of these non-commutative gauge theories is that there is a critical length in the
theory in which for distances larger than this length the effects of non-commutativity become
important and for smaller distances these effects are negligible. Therefore we would expect to see
this kind of non-commutativity in large distances which might be relevant in cosmology.
We also study M5-brane wrapping on 11-dimensional Melvin universe and its descendant theories upon
compactifying on a circle.
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