Wilson Loop and Dimensional Reduction in Non-Commutative Gauge Theories

Using the AdS/CFT correspondence we study UV behavior of Wilson loops in various noncommutative gauge theories. We get an area law in most cases and try to identify its origin. In D3 case, we may identify the the origin as the D1 dominance over the D3: as we go to the boundary of the AdS space, the effect of the flux of the D3 charge is highly suppressed, while the flux due to the D1 charge is enhenced. So near the boundary the theory is more like a theory on D1 brane than that on D3 brane. This phenomena is closely related to the dimensional reduction due to the strong magnetic field in the charged particle in the magnetic field. The linear potential is not due to the confinement by IR effect but is the analogue of Coulomb's potential in 1+1 dimension.