Strongly coupled plasma are quite interesting to study within
the framework of AdS/CFT, because of its possible relevance to
quark-gluon plasma one observes in heavy-ion collisions . Although the
plasma is studied by perturbing it and observing its linear responses,
sometimes the situation demands going beyond the linearized approximation
and taking back reactions to the gravity equations of motion into
account. In this talk I will focus on one of my collaborative project in
which we study a system which indeed needs full back reactions on the
metric. In this work we construct new gravity backgrounds holographic
dual to neutral plasma with U(1) global symmetry in the presence of
constant electric field, considering its full back-reactions to the
metric. As the electric field and the induced current cause a net energy
in-flow to the system, the plasma is continually heated up and the
corresponding gravity solution has an expanding horizon. After proposing
a consistent late-time expansion scheme, we present analytic solutions in
the scheme up to next-leading order, and our solutions are new
time-dependent solutions of 5D asymptotic AdS
Einstein-Maxwell(-Chern-Simons) theory. To extract dual CFT stress tensor
and U(1) current from the solutions, we perform a rigorous holographic
renormalization of Einstein-Maxwell-Chern-Simons theory including full
back-reactions, which can in itself be an interesting addition to
literatures. As by-products, we obtain interesting modifications of
energy-momentum/current Ward identities due to the U(1) symmetry and its
triangle anomaly.
