Employing new precision data of the equation of state of the SU(3) Yang-Mills theory (gluon plasma) the dilaton potential of a gravity-dual model is adjusted in the temperature range (1-10)T c within a bottom-up approach. The ratio of bulk viscosity to shear viscosity follows then as ζ /η ≈ π v 2 s for v 2 s < 0.2 and achieves a maximum value of 0.94 at v 2s is the non-conformality measure and v 2 s is the velocity of sound squared, while the ratio of shear viscosity to entropy density is known as (4π ) −1 for the considered set-up with Hilbert action on the gravity side.

Supplementing the holographic Einstein-Maxwell-dilaton model of [1,2] by input of lattice QCD data for 2+1 flavors and physical quark masses for the equation of state and quark number susceptibility at zero baryo-chemical potential we explore the resulting phase diagram over the temperature-chemical potential plane. A first-order phase transition sets in at a temperature of about 112 MeV and a baryo-chemical potential of 612 MeV. We estimate the accuracy of the critical point position in the order of approximately 5 − 8 % by considering parameter variations and different low-temperature asymptotics for the second-order quark number susceptibility. The critical pressure as a function of the temperature has a positive slope, i.e. the entropy per baryon jumps up when crossing the phase border line from larger values of temperature/baryo-chemical potential, thus classifying the phase transition as a gas-liquid one. The updated holographic model exhibits in-and outgoing isentropes in the vicinity of the first-order phase transition.

A dilaton potential is adjusted to recently confirmed lattice QCD thermodynamics data in the temperature range (0.7 . . . 3.5)T c where T c = 155 MeV is the pseudocritical temperature. The employed holographic model is based on a gravity-single-field dilaton dual. We discuss conditions for enforcing (for the pure gluon plasma) or avoiding (for the QCD quark-gluon plasma) a first-order phase transition, but still keeping a softest point (minimum of sound velocity).