Quantum field theory in curved spacetime

Abstract

We will look at working of quantum fields in the curved spacetime which is a frame work that includes all fundamental interactions while not requiring that gravity be quantized. String theory provides us the best possible tool to help in the unification of quantum field theory and gravity. The most celebrated idea of AdS/CFT duality, conjectured by Maldacena is a nice way to see it, which will also be the topic we will work on. The constructions of the bulk fields in terms of the boundary fields for di↵erent set tings have been carried out here. We look at the anti deSitter and deSitter cases and review some calculations in di↵erent coordinate systems for them. We employ the method of HKLL reconstruction. We carry on this construction over to the case of D1 branes and work in the 10 dimensional near horizon geometry dimensionally reduced to 3 dimensions. We look at a scalar field in this background and find its solution for di↵erent cases and develop a construction for it in terms of the boundary field theory, for the case of (horizon)ro ! 0.