Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT

Abstract

We present holographic descriptions of thermalization in conformal field theories using probe D-branes in AdS X S space-times. We find that the induced metrics on Dp-brane worldvolumes which are rotating in an internal sphere direction have horizons with characteristic Hawking temperatures even if there is no black hole in the bulk AdS. The AdS/CFT correspondence applied to such systems indeed reveals thermal properties such as Brownian motions and AC conductivities in the dual conformal field theories. We also use this framework to holographically analyze time-dependent systems undergoing a quantum quench, where parameters in quantum field theories, such as a mass or a coupling constant, are suddenly changed. We confirm that this leads to thermal behavior by demonstrating the formation of apparent horizons in the induced metric after a certain time.

Figures (10)

• Figure 1: A schematic diagram for our non-equilibrium systems in the AdS/CFT. Here we concentrate on the example of a probe D7-brane in $AdS_5\times S^5$ discussed in section 4. The other cases can be interpreted in the same way after obvious modifications.
• Figure 2: We present the schematic pictures of (a) a thermal D1-brane solution extended in Poincare $AdS_5$, (b) a suspended D1-brane solution in Poincare $AdS_5$, (c) a D1-brane solution in global $AdS_5$, and their CFT duals: (a$^\prime$),(b$^\prime$) and (c$^\prime$). The D1-branes are all rotating along a great circle in the $S^5$.
• Figure 3: The profile of a rotation D1-brane in AdS at some given time in the $(x^4=r \sin \varphi, x^5=r\cos \varphi)$ plane. The time evolution is obtained by rotating the profile.
• Figure 4: The frequency dependence of the conductivity. Four lines are depicted for $\rho = 10, \sqrt{10},1$ and $1/\sqrt{10}$, respectively when $\omega =1$. The real part of the conductivity approaches to Re $\sigma ({\nu}) =1$ line as $\rho$ decreases, while the imaginary part becomes zero.
• Figure 5: The shapes of the rotating D7-brane with $\omega =1$. In the left panel where we consider $g'=0$ case, we depict the curves for $a=1.01,1.1,1.2$ and $1.5$. In the right panel where we consider $g'\neq 0$, we depict them for $\alpha =\pi/2, \pi/2.1, \pi/2.5, \pi/3, \pi/4, \pi/10$. The dotted regions are inside the horizon.