On the Supergravity Description of Wilson Loop in Non-commutative Dipole Field Theory

TL;DR

This paper investigates the Wilson loop in non-commutative dipole field theory using supergravity, revealing a Coulomb potential at all distances and analyzing the transition from static to moving string configurations.

Contribution

It provides an exact interquark potential in non-commutative dipole field theory by considering moving dual strings, improving upon previous static analyses.

Findings

Interquark potential exhibits Coulomb behavior at all distances.

Dual string transitions from static to moving at short distances.

Similar transition observed in electric dipole systems.

Abstract

The Wilson loop in the non-commutative dipole field theory is re-examined within the framework of dual gravity description. In contrast to the previous investigations, we let the dual string be moving along the deformed $S^5$ and find the exact expression of the interquark potential. The potential shows a Coulomb behavior at all distance and does not have a minimum distance between quarks, which exhibits in the static configuration. After comparing the potential of the static and moving configurations we find that while the dual string is static at long distance it will transit to a moving configuration at short distance. We also analyze an electric dipole system and find that it shows a similar transition property. Finally, we mention the unsuitable approximation made in the previous paper [hep-th/0701069] and find that the interquark potential in a gauge theory with a non-constant non-commutativity has a Coulomb behavior at all distance.