Holographic Description of Glueball and Baryon in Noncommutative Dipole Gauge Theory

We study the glueball spectrum in the supersymmetric and non-supersymmetric 4D non-commutative dipole gauge theory from the holographic description. We adopt the semiclassical WKB approximation to solve the dilaton and antisymmetric tensor field equations on the dual supergravity backgrounds to find the analytic formula of the spectrum of $0^{++}$ and $1^{--}$ glueballs, respectively. In the supersymmetric theory we see that the dipole length plays the intrinsic scale which reflects the discrete spectrum therein. In the non-supersymmetric theory, the temperature (or the radius of compactification) in there will now play the intrinsic scale and we see that the dipole has an effect to produce attractive force between the gluons within the glueball. We also study the confining force between the quarks within the baryon via strings that hang into the dipole deformed AdS geometry and see that the dipole could also produce an attractive force between the quarks. In particular, we find that the baryon has two phases in which a big baryon is dual to the static string while a small baryon is described by a moving dual string .