Abstract
Motivated by a semi-holographic approach to the dynamics of quark-gluon plasma which combines holographic and perturbative descriptions of a strongly coupled infrared and a more weakly coupled ultraviolet sector, we construct a hybrid two-fluid model where interactions between its two sectors are encoded by their effective metric backgrounds, which are determined mutually by their energy-momentum tensors. We derive the most general consistent ultralocal interactions such that the full system has a total conserved energy-momentum tensor in flat Minkowski space and study its consequences in and near thermal equilibrium by working out its phase structure and its hydrodynamic modes.
Highlights
In terms of strongly coupled models, such as N = 4 super Yang-Mills theory as described by AdS/CFT duality [3]
In the following we investigate the linearized perturbations of the full hybrid system about thermal equilibrium for given values of the hydrodynamic transport coefficients within the two subsystems, i.e., parameterising their energy-momentum tensors to first order in the gradient expansion according to tμν = ( 1 + P1)uμuν + P1gμν − 2η1σμν − ζ1θP μν, (4.1)
In the semi-holographic approach to the dynamics of quark-gluon plasma with its coexistence of strongly and weakly interacting sectors it has been proposed to introduce a coupling of the respective marginal operators [6, 7, 17]
Summary
2.1 Semi-holography and democratic coupling We consider a dynamical system S in a fixed background metric gμ(Bν) (to be set to the Minkowski metric ημν eventually) which consists of two subsystems S1 and S2. Motivated by the semi-holographic approach in the democratic formulation [17], the two subsystems are assumed to have covariant dynamics with respect to individual effective metrics gμν and gμν, respectively.. Let the theory describing the non-perturbative sector be a (strongly coupled holographic) Yang-Mills theory with the coupling gYM whereas gYM is the coupling of the perturbative sector These mutual deformations by scalar operators lead to the modified Ward identities (we turn off other couplings including the effective metric couplings for purpose of illustration). In [17], the most general scalar couplings of the form have been explored and a toy construction has been done to illustrate how these “hard-soft” couplings (such as α) along with the parameters of the holographic classical gravity determining Shol can be derived as functions of the perturbative couplings in Spert via simple consistency rules. We extend and correct the democratic effective metric type couplings set up in [17]
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