Wilson-t’Hooft Loops in Finite-Temperature Non-commutative Dipole Field Theory from Dual Supergravity

We first study the temporal Wilson loop in the finite-temperature non-commutative dipole field theory from the string/gauge correspondence. The associated dual supergravity background is constructed from the near-horizon geometry of near-extremal D-branes, after applying T-duality and smeared twist. We investigate the string configuration therein and find that while the temperature produces a maximum distance Lmax in the interquark distance the dipole in there could produce a minimum distance Lmin. The quark boundary pair therefore could be found only if their distance is between Lmin and Lmax. We also show that, beyond a critical temperature the quark pair becomes totally free due to screening by thermal bath. We next study the spatial Wilson loop and find the confining nature in the zero temperature 3D and 4D non-supersymmetry dipole gauge theory. The string tension of the linear confinement potential is obtained and found to be a decreasing function of the dipole field. We also investigate the associated t’Hooft loop and determine the corresponding monopole anti-monopole potential. The conventional screening of magnetic charge which indicates the confinement of the electric charge is replaced by a strong repulsive however. Finally, we show that the dual string which is rotating along the dipole deformed S will behave as a static one without dipole field, which has no minimum distance and has larger energy than a static one with dipole field. We discuss the phase transition between these string solutions.