Transport Coefficients in Yang-Mills Theory and QCD

Abstract

We calculate the shear viscosity over entropy density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently we provide a first estimate for η/s in QCD.PACS numbers: 12.38. Aw, 11.10.Wx , 11.15.Tk Introduction -The experimental heavy-ion programs at RHIC [1,2] and at the LHC [3] explore the physics of the quark-gluon plasma (QGP). It turns out that the dynamics of the hot plasma created in heavy-ion collisions is well-described by hydrodynamics. Therefore, the determination of transport coefficients in the QGP is of great interest. One aspect is that the inference of the initial state physics requires a precise description of the hydrodynamical evolution, which in turn depends on transport coefficients as microscopic input, [4]. In particular, the viscosity over entropy ratio η/s governs the efficiency of the conversion of the initial spatial anisotropy into a momentum anisotropy of the final state.For the determination of η/s and its temperature dependence in the quark-gluon plasma, theoretical approaches face several challenges.The temperature regimes below and above the critical temperature T c are characterised by different degrees of freedom, and for temperatures T 2T c non-perturbative effects become important. Of particular interest is the vicinity of T c , where the minimum for η/s is expected [5,6]. A universal lower bound for η/s of 1/4π was conjectured in [7] using the AdS/CFT correspondence. Indeed, measurements of the elliptic flow v 2 indicate a value for η/s which is of the order of this lower bound [8]. The bound has been tested theoretically with several methods for the QGP [9-15], but also for other potentially perfect liquids, such as ultracold atoms [16][17][18].The Kubo formulae relate η to the energy-momentum tensor (EMT) [19]. Spectral functions are real-time quantities and cannot be obtained directly from Euclidean correlation functions. However, the direct calculation of real-time correlation functions represents a notoriously difficult problem in non-perturbative approaches to quantum field theory. Even though first computations in this direction have been performed e.g. in [20,21], we shall utilise Euclidean correlation functions within a numerical analytic continuation.In this work we study the shear viscosity over entropy ratio η/s in pure SU (3) Landau gauge Yang-Mills (YM) theory within the approach set-up in [9]. In the present

Consistency of Perfect Fluidity and Jet Quenching in Semi-Quark-Gluon Monopole Plasmas

“…Including such a hadronic component, as we will study in the future, is necessary for a more accurate description of a likely rapidly increasing η/s in the low-T region, as indicated by e.g. a recent work [82]. Summary.…”

“…The AdS/CFT perfect fluidity limit η/s = 1/4π is marked as SYM. The shaded line is the Hadron Resonance Gas (HRG) η/s from [82]. The falling of sQGMP's η/s below 1/4π is due to the limitation of kinetic theory estimate of η/s in the low E extrapolation of T 3 /q(E ∼ 3T, T ) [6].…”

Finite-temperature gluon spectral functions from $$N_f=2+1+1$$ N f = 2 + 1 + 1 lattice

“…Equation (10) has been used and checked in continuum computations in many instances in the literature; see e.g. [19,21,23,40]. On the other hand, since the derivation of Eq.…”

“…On the other hand such real-time properties can also be accessed via the spectral functions of the fundamental constituents of QCD, gluons and quarks; see e.g. [14,[19][20][21][22][23][24][25].…”

“…Secondly gluon spectral functions play a vital role in the self-consistent computation of transport coefficients in functional approaches to QCD [19,21], such as the functional renormalization group or Dyson-Schwinger approaches. If the gluon spectral function is known, it may serve as input to a closed set of real-time evolution equations for quark and gluon degrees of freedom, from which relevant quantities, such as energy-momentum correlation functions may be computed.…”