Holographic calculation of the electric conductivity of the strongly coupled quark-gluon plasma near the deconfinement transition

Abstract

The frequency dependent conductivity σ(ω) of the strongly coupled QuarkGluon Plasma (QGP) is estimated using a bottom up holographic model that can adequately describe recent lattice data for QCD thermodynamics at zero chemical potential. Different choices for the coupling between the bulk gauge field and the other bulk fields that define the background (the metric and a scalar field) are used in order to fit the lattice data for the electric charge susceptibility χ Q 2 /T 2 . The ratio σ DC /T is found to vary near the deconfinement transition in a way that is similar to recent lattice results. This model is used to compute the charge diffusion coefficient D of the strongly coupled plasma. We find that the dimensionless combination DT has the same type of temperature dependence displayed by σ DC /T and, thus, charge diffusion is suppressed at low temperatures. The frequency dependent conductivity σ(ω) reveals some nontrivial structure for values of the temperature near the phase transition. None of these structures appear in the associated Euclidean correlator, which we also compute. Our results suggest that the conformal invariance violation near the QCD deconfinement phase transition may be seen in the Euclidean correlator through a downward shift of its value at the minimum, which gives a rough estimate of the temperature dependence of the DC conductivity in the plasma.arXiv:1311.6675v1 [hep-th]

Temperature dependent transport coefficients in a dynamical holographic QCD model

“…At high temperature, σ el /T increases slowly and tends to 0.05 from below. Furthermore, in figure 6, we also compare our results to that of the holographic model in [60], where the authors build up a non-conformal bottom-up holographic model to mimic the N f = 2+1 thermodynamics. Different from our approach to introduce flavor dynamics described in section 2, they work in the gravitondilaton system but constrain the dilaton potential to produce the correct equations of state of N f = 2 + 1 QCD.…”

“…Here we compare our results to the quenched lattice results: the Black dot [55] and purple dot [56]. The lattice simulations including flavor effect are also shown in the blue dot [57] and the green dots [58], comparing to the holographic results(dashed cyan line) from [60](data extracted from [59]). We have taken the electric charge e 2 = 4π/137 when extracting the data.…”

“…The electric conductivity describes the response of the system to external electric field and is responsible for the production of the collective flow of charged particles [51]. The temperature dependent behavior of σ el has been studied in perturbative calculations [9,52,53], lattice simulations [54][55][56][57][58], effective models [59] as well as holographic studies [60]. The leading high temperature dependence of electric conductivity has been determined perturbatively as σ el ≃ CT /(e 2 log e −1 ) [9], with e the electric charge and C ≃ 12 4 ζ(3) 2 π −3 N leptons 3π 2 +32N species depending on N leptons the numbers of leptonic charge carriers and N species the sum over fermions weighted by the square of their electric charge assignments.…”

Hydrodynamic transport coefficients for the non-conformal quark-gluon plasma from holography

“…The Einstein+Scalar holographic model has been successfully used in several other works to understand the temperature dependence of quantities evaluated near the crossover phase transition of the QGP such as the bulk viscosity [78], the expectation value of the Polyakov loop [79,80], the energy loss of heavy and light quarks [81][82][83], the electric conductivity [84], and the Debye screening mass [85].…”

Dynamical versus equilibrium properties of the QCD phase transition: A holographic perspective

“…These holographic results at vanishing baryon density constitute an update of the results first published in Ref. [82], which were based on an older version of the holographic model (without chemical potential). We note that the EMD results for the electric conductivity of the QGP, which are predictions of the model, are much closer to the lattice QCD results from Ref.…”