Magnetic effects on chiral phase transition have been investigated in a modified soft-wall AdS/QCD model, in which the dilaton field is taken to be negative at the ultraviolet region and positive at the infrared region as in Phys. Rev. D 93 (2016) 101901 and JHEP 04 (2016) 036. The magnetic field is introduced into the background geometry by solving the Einstein-Maxwell system. After embedding the magnetized background geometry into the modified soft-wall model, the magnetic field dependent behavior of chiral condensate is worked out numerically. It is found that, in the chiral limit, the chiral phase transition remains as a second order at finite magnetic field B, while the symmetry restoration temperature and chiral condensate decrease with the increasing of magnetic field in small B region. When including finite quark mass effect, the phase transition turns to be a crossover one, and the transition temperature still decreases with increasing magnetic field B when B is not very large. In this sense, inverse magnetic catalysis effect is observed in this modified soft-wall AdS/QCD model.

We study confinement-deconfinement phase transition for heavy quarks in a soft wall holographic QCD model. We consider a black hole background in an EinsteinMaxwell-scalar system and add probe open strings to the background. Combining the various configurations of the open strings and the phase structure of the black hole background itself, we obtain the confinement-deconfinement phase diagram for heavy quarks in the holographic QCD model.

Abstract:We consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic gauge function and a dilaton potential. A family of analytic solutions is obtained by the potential reconstruction method. We then study its holographic dual QCD model. After fixing the kinetic gauge function by requesting the linear Regge spectrum of mesons, we calculate the free energy to obtain the phase diagram of the holographic QCD model.

We study confinement-deconfinement phase transition in a holographic soft-wall QCD model. By solving the Einstein-Maxwell-scalar system analytically, we obtain the phase structure of the black hole backgrounds. We then impose probe open strings in such background to investigate the confinementdeconfinement phase transition from different open string configurations under various temperatures and chemical potentials. Furthermore, we study the Wilson loop by calculating the minimal surface of the probing open string world-sheet and obtain the Cornell potential in confinement phase analytically.

We address the well-posedness of the primitive equations of the ocean with continuous initial data. We show that the splitting of the initial data into a regular finite energy part and a small bounded part is preserved by the equations, thus leading to existence and uniqueness of solutions.