Residues of correlators in the strongly coupledN=4plasma

Abstract

Quasinormal modes of asymptotically AdS black holes can be interpreted as poles of retarded correlators in the dual gauge theory. To determine the response of the system to small external perturbations it is not enough to know the location of the poles: one also needs to know the residues. We compute them for R-charge currents and find that they are complex except for the hydrodynamic mode, whose residue is purely imaginary. For different quasinormal modes the residue grows with momentum q, whereas for the hydrodynamic mode it behaves as a damped oscillation with distinct zeroes at finite q. Similar to collective excitations at weak coupling the hydrodynamic mode decouples at short wavelengths. Knowledge of the residues allows as well to define the time scale τ H from when on the system enters the hydrodynamic regime, restricting the validity of hydrodynamic simulations to times t > τ H .

Holographic quark gluon plasma with flavor

“…Note that this behavior is still present if we set µ = 0 such that the diffusion pole lies on the imaginary frequency axis, but the peak of the spectral function appears at a shifted position ω ∝ ±Dq 2 . A computation of the residues (see also [49]) at µ = 0 confirms this behavior for the correlators G 00 and G 33 while the mixed correlator G 03 gives a peak in the spectral function centered at w = 0. Physical interpretation The physical interpretation of this frequency or energy shift leads us into the internal flavor space.…”

“…Although this is a crude approach (the resonances do not have the Lorenz shape but are deformed, cf. [49]) the location and width of the peaks are captured quite well (optical check). The height of the peaks might be a subject to discussion since the unknown parameter A varies roughly between 0.1 and 10 over the scanned parameter range.…”

“…Further studies have shown that on the gravity side a geometric transition (see section 2.1.1) corresponds to a deconfinement transition for the fundamental matter in the thermal gauge theory. At the moment the flavored extension of the relation between hydrodynamics and black hole physics is under intense investigation [43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61, incomplete list of closely related work]. So far the effect of finite chemical baryon potential in the gauge theory and the structure of the phase diagram of these theories have been explored.…”

Electromagnetic response of strongly coupled plasmas

“…7 Previous studies have shown that plasmas described with the gauge/gravity correspondence have in general an infinite set of discrete quasi-normal (complex valued) self-frequencies [51][52][53][54][55][56], that appear as poles in the two-point retarded correlation function of the currents. In this paper we are interested to couple these quasi-normal modes of the plasma to an external electromagnetic field and study the possible electromagnetic modes supported by the system.…”

“…The retarded correlation function accounting for the electromagnetic response of the plasma presents poles at specific values for the momentum and frequency of the external perturbation. Such poles correspond in the dual gravitational picture to quasi-normal modes of the black hole solution (see for instance [55,56,58,62,[66][67][68][69][70]). To find the dispersion relations between q and w of the above-mentioned quasi-normal modes it is enough to look at the zeros of the inverse of the correlation function.…”