Abstract
We exploit the AdS/CFT correspondence to investigate thermalization in an N=2 strongly coupled gauge theory including massless fundamental matter (quark). More precisely, we consider the response of a zero temperature state of the gauge theory under influence of an external electric field which leads to a time-dependent current. The holographic dual of the above set-up is given by introducing a time-dependent electric field on the probe D7-brane embedded in an AdS5×S5 background. In the dual gravity theory an apparent horizon forms on the brane which, according to AdS/CFT dictionary, is the counterpart of the thermalization process in the gauge theory side. We classify different functions for time-dependent electric field and study their effect on the apparent horizon formation. In the case of pulse functions, where the electric field varies from zero to zero, apart from non-equilibrium phase, we observe the formation of two separate apparent horizons on the brane. This means that the state of the gauge theory experiences two different temperature regimes during its time evolution.
Highlights
AdS/CFT correspondence, or more generally gauge/gravity duality, has been extensively used to study the issue of quantum quench in strongly coupled gauge theories [13]
By probe limit we mean that the back-reaction of the brane on the background is negligible or, in other words, the background we are dealing with remains unchanged1
If one turns on a constant external electric field on the probe D-brane, matter fields will couple to the electric field and an electric current emerges on the probe brane2 [8]
Summary
We present a short review of holographic electric field quench. This family of quenches can be described as a suddenly applied electric field to a system that induces nontrivial dynamics and may lead to interesting results such as thermalization. In order to analyze these nonequilibrium transitions, the AdS/CFT correspondence for N = 2 supersymmetric QCD-like, at zero temperature, has been used This time-dependent phenomena is described in the gravity theory by the dynamics of a D7-brane, supersymmetrically embedded in an AdS5 × S5 spacetime, subject to a dynamical electric field. On the other hand in the more interesting case of a time-dependent electric field that rises up from zero to a constant value of say E0, called a quench, it is expected that the system would go through a non-equilibrium phase and only asymptotically approach the same current as in the case of a constant electric field. In the static massless case, it is shown in [9] that for constant electric fields, the effective metric [17], due to gauge fluctuations, induces a metric on the D7-brane that exhibits a black hole singularity at zp = E0−1/2. Due to linearity of (2.13) in vt and vz, only the ratio vt/vz is needed which can be obtained from the nullity equation for vμ
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