Interacting quantum fields in various charts of anti-de Sitter spacetime

Abstract

The goal of the present paper is to understand whether it is possible to define interacting quantum field theory in global anti-de Sitter spacetime with Lorentzian signature, in its covering spacetime (whose time coordinate is not periodic) and in its Poincaré patch. We show that in global anti-de Sitter spacetime there are certain problems with defining quantum field theory properly. This is due to an additional UV singularity of the Feynman propagator which is sitting on the light cone emanating from the antipodal point of the source. There is no such singularity in flat spacetime. At the same time quantum field theory in the Poincaré region of the anti-de Sitter (AdS) spacetime can be well defined and is related to the one in Euclidean AdS via the analytical continuation. In principle one can also define and analytically continue quantum field theory in the covering anti-de Sitter spacetime. However, to do that one has to use an unusual iϵ prescription in the Feynman propagator which cannot be used in loop calculations in nonstationary situations.