A holographic view on physics out of equilibrium

Abstract

We review the recent developments in applying holographic methods to understand non-equilibrium physics in strongly coupled field theories. The emphasis will be on elucidating the relation between evolution of quantum field theories perturbed away from equilibrium and the dual picture of dynamics of classical fields in black hole backgrounds. In particular, we discuss the linear response regime, the hydrodynamic regime and finally the non-linear regime of interacting quantum systems. We also describe how the duality might be used to learn some salient aspects of black hole physics in terms of field theory observables.

Figures (13)

• Figure 1: Rough indication of the regimes of validity of the linear response theory and the fluid/gravity correspondence, in the space of perturbations from global thermodynamic equilibrium, labeled by the amplitude of perturbations $A$ and the wave number (or frequency) $k = \ell_{\rm mfp}/L$, relative to the microscopic scale. We have indicated the relevant sections of the paper where the different regimes are discussed from the holographic perspective.
• Figure 2: The trailing string solution in Schwarzschild-AdS$_{4}$ spacetime. The curves are drawn for differing values of the quark velocity $v$ (specifically from right to left, $v=0, 0.15, 0.5, 0.8$, and $0.99999$) on the boundary.
• Figure 3: The spiral string solution in AdS$_5$ spacetime corresponding to quark undergoing a circular motion. The curves are drawn for differing values of the quark velocity $v$ on the boundary (values of $v$ and color-coding same as in Fig. \ref{['fig:trstring']}). The small black circle on the top is the quark's trajectory on the AdS boundary; the vertical direction corresponds to the bulk radial direction.
• Figure 4: The causal structure of the spacetimes dual to fluid mechanics illustrating the tube structure. The dashed line denotes the future event horizon ${\cal H}^+$ generated by $\xi^A$, while the shaded tube indicates the region of spacetime over which the solution is well approximated by a tube of the uniform black brane.
• Figure 5: Conformal Soliton energy density (left) and dual geometry (right). On left, $T_{00}(t,r)$ is plotted as a function of boundary time $t$ and boundary radial variable $r$. On right, the outer cylinder represents the AdS boundary, the inner (red) cylinder corresponds to the global Schwarzschild-AdS$_{}$ event horizon, which coincides with the apparent horizon of the conformal soliton, whereas the flared (blue) surface is the actual event horizon.