Numerical solutions of non-equilibrium quantum field theories via gauge/gravity duality

We build on the anti-de Sitter/conformal field theory correspondence in theoretical physics. This conjecture gives a correspondence between gravitational dynamics (rooted in Einstein?s general relativity) and quantum field theory. By considering Einstein?s field equations for a time-dependent gravity configuration, we will find solutions which provide new information about the dual non-equilibrium quantum field theory at strong coupling. The research will begin by taking Einstein's equations and deriving the partial differential equations in the special case at hand, in anti-de Sitter space-time. We would bring mathematics to bear on this problem by writing the problem as an initial boundary value problem. In particular we plan to write this as an hyperbolic problem by a conformal transformation of the 3-metric [1]. This is in principle possible to do in the case we are interested in. It leads to a first order hyperbolic system for which we will derive the eigenstructure of this system [2]. This leads to a form of the problem for which the theoretical and numerical knowledge of Prof. Klingenberg and Prof. Risebro can come to bear. Not only can the accuracy of the numerical method be proven, but also it will be possible to perform reliable numerical simulations yielding predictions for observables in the dual non-equilibrium quantum field theory that were not accessible for numerical study before, such as the entanglement entropy in steady state systems in three and more dimensions.