Shear channel correlators from hot charged black holes

TL;DR

The paper computes full, frequency- and momentum-dependent shear-channel retarded Green's functions for a (2+1)D boundary theory at finite temperature and density using a holographic dual described by a non-extremal RN AdS4 black hole. Employing gauge-invariant master fields and infalling boundary conditions, it extracts the Green's functions from boundary data and verifies pole locations against bulk quasinormal modes. It reveals a rich pole structure with varying residues, including repulsion and clover-leaf crossings in pole trajectories, and characterizes large-wave and large-momentum behavior, along with the hydrodynamic diffusion pole in hatΠ−. The results illuminate non-hydrodynamic real-time dynamics in holographic matter and set the stage for extensions to the sound channel and zero-temperature regimes.

Abstract

We compute numerically the full retarded Green's functions for conserved currents in the shear channel of a (2+1)-dimensional field theory at non-zero temperature and density. This theory is assumed to be holographically dual to a non-extremal, electric Reissner-Nordstr\om AdS4 black hole with planar horizon. Using the holographic description we obtain results for arbitrary frequencies and momenta and survey the detailed structure of these correlators. In particular, we demonstrate the `repulsion' and `clover-leaf crossing' of their poles and stress the importance of the residues at the poles beyond the hydrodynamic regime. As a consistency check, we show that our results agree precisely with existing literature for the appropriate quasinormal frequencies of the bulk theory.

Figures (10)

• Figure 1: A comparison between density plots of $|\hat{\Pi}_{\pm}|$ on the complex $\textswab{w}$ plane (left panels) and the quasinormal frequencies for $\Phi_{\pm}$. The top row is for $\Phi_+$ and the bottom row is for $\Phi_-$. All plots have $\textswab{q}=1$ and $T/\mu=0.09$. As we discuss later, the on-axis modes are weaker but have been tested thoroughly against the quasinormal spectrum in a finer plot.
• Figure 2: A comparison between a surface plot of $|G_{xy,y}|$ on the complex $\textswab{w}$ plane (left) and the appropriate quasinormal frequencies. Both plots have $\textswab{q}=1$ and $T/\mu=0.09$.
• Figure 3: Surface plots of $\hat{\Pi}_{+}$ (top row) and $\hat{\Pi}_{-}$ (bottom row) on the complex $\textswab{w}$ plane at $\textswab{q}=1$, $T/\mu=0.09$. We show (from left to right) the real part, imaginary part and absolute value of each. All plots have the same orientation on the plane, as indicated.
• Figure 4: Surface plots of $| \hat{\Pi}_{+} |$ (left) and $| \hat{\Pi}_{-} |$ (right) on the $(\operatorname{Re}\textswab{w},\textswab{q})$ plane at $T/\mu=0.09$ to demonstrate the large $\textswab{w}$ and $\textswab{q}$ scaling. Note that we avoid $\textswab{q}=0$: in that case the symmetry is enhanced and so the master fields are different, as discussed in Edalati:2010hk.
• Figure 5: Slices through the $(\operatorname{Re}\textswab{w},\textswab{q})$ plane of $\hat{\Pi}_{+}$ (top row) and $\hat{\Pi}_{-}$ (bottom row) at $\textswab{q}=10^{-6}$ and $T/\mu=0.09$. The left and right panels show the real and imaginary parts, respectively.