Extended soft wall model with background related to features of QCD thermodynamics

The soft wall model is extended to accommodate at the same time (i) approximately linear ρ meson Regge trajectories at zero temperature T, (ii) various options for the thermodynamics with reference to QCD (cross over or second-order transition or first-order transition at Tc), and (iii) the appearance of vector meson states at T≤Tc. While the vector meson masses display some modest model dependence very near to Tc, they stay below Tc to good accuracy independent of the temperature, that is nearly as at T=0, thus being very consistent with the thermo-statistical models widely employed in analyses of the hadron yields in relativistic heavy-ion collisions in a region where baryon densitiy effects can be neglected and the vacuum hadron masses are used.