Equation of state and viscosities from a gravity dual of the gluon plasma

Abstract

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.

Cross-over versus first-order phase transition in holographic gravity–single-dilaton models of QCD thermodynamics

“…3 also unravels some uncomfortable features of the ansatz (8) with parameters adjusted to the lattice YangMills equation of state as in [28]: To catch the shape of thermodynamic quantities in the temperature range (0.7−10)T c , the ansatz (8) does not qualify to continue toward the deep IR region, since, e.g., v 2 s becomes negative for φ H 9.5, signaling the break-down of the ansatz's capabilities. (From the IHQCD viewpoint such a behavior is admissible: the point where v 2 s = 0 would signal a Hawking-Page phase transition to the p = 0 phase, and desirable: the model becomes zero-T confining [21].…”

“…2. Remarkable is the reduction of ζ /η by 50 % at T c in comparison with the SU(3) gluon plasma (YM) considered in [28]. To understand this difference, recall the adiabatic approximation of [20]:…”

“…In this respect, estimates of ζ /T 3 in various approaches are of contemporary interest. Remarkably, the ansatz (8) for the dilaton potential is the same as used in [28] (cf. [36] for a modified variant) to describe the SU(3) gluon plasma, which displays a first-order phase transition.…”

“…Remarkably, the ansatz (8) for the dilaton potential is the same as used in [28] (cf. [36] for a modified variant) to describe the SU(3) gluon plasma, which displays a first-order phase transition. (This is actually not so surprising, as [20] has demonstrated that a two-parameter ansatz for the potential allows either for a cross-over, or a first-order phase transition or a second-order transition, depending on the choice of the parameters.…”

Bulk Viscosity of the Gluon Plasma in a Holographic Approach

“…Optimum adjustment to lattice data As shown in [15], a perfect matching to lattice data is accomplished by the potential (4) for ∆ = 3.7650 and γ = 0.6580 when including the polynomial distortions c 2n ; omitting the latter ones (with ∆ = 3.5976 and γ = 0.6938) the match is near-perfect, see left panel…”