Abstract
We consider holographic thermalization in the presence of a Weyl correction in five dimensional AdS space. We first obtain the Weyl corrected black brane solution perturbatively, up to first order in the coupling. The corresponding AdS-Vaidya like solution is then constructed. This is then used to numerically analyze the time dependence of the two point correlation functions and the expectation values of rectangular Wilson loops in the boundary field theory, and we discuss how the Weyl correction can modify the thermalization time scales in the dual field theory. In this context, the subtle interplay between the Weyl coupling constant and the chemical potential is studied in detail.
Highlights
Equilibrium, and calculate the “thermalization time.” In a class of examples, this issue has been resolved holographically by constructing a time-dependent gravity solution in AdS space which describes the formation of a black hole at late times
The corresponding AdS-Vaidya like solution is constructed. This is used to numerically analyze the time dependence of the two point correlation functions and the expectation values of rectangular Wilson loops in the boundary field theory, and we discuss how the Weyl correction can modify the thermalization time scales in the dual field theory
The other fact that motivates the study of non-equilibrium dynamics from the gauge/gravity duality, is the experimental input from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC)
Summary
We first write down the model action and construct the black brane solution solving the Einstein and Maxwell equations. To describe the thermalization process in the field theory, we need to create an AdS black brane from a pure AdS space in the dual gravity sector This formation of black branes is well-described in literature [23, 27, 28] by modeling the spacetime with a AdS-Vaidya metric which desribes the collapse of a thin shell of charged matter from the boundary, into the bulk interior. To study the effect of the Weyl coupling on thermalization, we need to construct a similar AdS-Vaidya type metric which at early time would correspond to a pure AdS space, and at late times would merge to the Weyl-corrected black brane metric after the shell collapses. Considering this external matter source, the Einstein and Maxwell equation can be written as,
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