Violation of the Holographic Viscosity Bound in a Strongly Coupled Anisotropic Plasma

Abstract

We study the conductivity and shear viscosity tensors of a strongly coupled N = 4 super-YangMills plasma which is kept anisotropic by a θ parameter that depends linearly on one of the spatial dimensions. Its holographic dual is given by an anisotropic axion-dilaton-gravity background and has recently been proposed by Mateos and Trancanelli as a model for the pre-equilibrium stage of quark-gluon plasma in heavy-ion collisions. By applying the membrane paradigm which we also check by numerical evaluation of Kubo formula and lowest lying quasinormal modes, we find that the shear viscosity purely transverse to the direction of anisotropy saturates the holographic viscosity bound, whereas longitudinal shear viscosities are smaller, providing the first such example not involving higher-derivative theories of gravity and, more importantly, with fully known gaugegravity correspondence.PACS numbers: 11.25. Tq, 11.10Wx, 12.38.Mh Introduction. Hydrodynamic simulations of heavyion collisions suggest [1] that the produced quark-gluon plasma is behaving like an almost perfect fluid with a ratio of shear viscosity over entropy density not far from the famous result /4π associated with the membrane paradigm of black holes [2] and which holographic gaugegravity duality maps to the corresponding quantity of maximally supersymmetric Yang-Mills theory in the limit of infinite color number and infinite 't Hooft coupling [3,4]. This value has been conjectured to form the lower bound for any realistic matter [5]. It was found to be saturated universally [6,7] in dual theories involving an isotropic horizon described by Einstein gravity. Values above this bound are obtained when corrections due to finite coupling strength are included [8], but it has been shown that values violating the bound can arise in higherderivate gravities [9], although so far no complete gaugegravity correspondence has been established for finite violations.

The shear channel spectral function in hot Yang-Mills theory

“…Next, we introduce the notation 12) in which the one-and two-loop functions f J 0 x and f I 0 x , corresponding to the integrals encountered in the bulk case, can be read off from [17] and are for completeness reproduced in appendix A.2. Using eq.…”

“…At the same time, a reliable nonperturbative determination of transport coefficients, in principle available from the zero frequency limit of the corresponding (Minkowskian) spectral functions, has proven extremely challenging, as the lattice approach is restricted to the Euclidean formulation of the theory [7][8][9]. As a result, a considerable amount of attention has shifted towards the gauge/gravity duality, which has in particular led to the famous claim of the QGP being a nearly 'ideal' fluid, with a shear viscosity to entropy ratio close to the conjectured limit η/s ≥ 1/(4π) [10] (see also [11,12] for some interesting recent developments).…”

Holographic RG flow of the shear viscosity to entropy density ratio in strongly coupled anisotropic plasma

“…And, the horizon u h and the entropy density s are related to the temperature T by [21] 2) to second order in h M N , and also using the gauge h M u = 0, we'll have [22] …”

“…Our five dimensional axion-dilaton gravity bulk action, which is a type IIB supergravity action where the Ramond-Ramond (RR) field, the axion, is a 0-form potential which is the 'magnetic' dual of the 8-form potential which couples to D7-branes 'electrically', is [20][21][22] …”

On the infrared behavior of the shear spectral function in hot Yang-Mills theory

“…[1][2][3][4][5]). Despite the strong experimental and phenomenological motivation, a nonperturbative first principles tool to predict its value is, however, still lacking, even though an extensive amount of work has been devoted to the topic in the weak coupling [6,7], lattice [8][9][10] and gauge/gravity frontiers [11][12][13]. The main issue preventing a straightforward lattice determination of the parameter is its inherently Minkowskian nature: according to the Kubo formulae, the viscosity is available as the zero frequency limit of the corresponding spectral function,…”