Wilson Loop and Dimensional Reduction in Non-Commutative Gauge Theories

TL;DR

This paper investigates the UV behavior of Wilson loops in noncommutative gauge theories using AdS/CFT, revealing an area law and a D1 dominance near the boundary, akin to dimensional reduction under strong magnetic fields.

Contribution

It demonstrates the origin of the area law in noncommutative gauge theories as D1 brane dominance and links this to dimensional reduction effects similar to strong magnetic fields.

Findings

Wilson loops exhibit an area law in noncommutative gauge theories.

Near the boundary, D1 brane effects dominate over D3, leading to dimensional reduction.

The linear potential resembles Coulomb's law in 1+1 dimensions.

Abstract

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.