On interacting quantum fields in various charts of anti de Sitter space-time

TL;DR

This paper investigates the challenges of defining interacting quantum field theories in various regions of anti de Sitter space-time, highlighting singularities in global AdS and the well-posedness in Poincare patches.

Contribution

It identifies specific UV singularities in global AdS and clarifies conditions under which quantum field theory can be consistently defined in different AdS regions.

Findings

Global AdS has UV singularities on the light-cone from antipodal points.

Quantum field theory in Poincare AdS can be well-defined and related to Euclidean AdS.

Analytic continuation in covering AdS requires an unusual $i\epsilon$-prescription.

Abstract

The goal of the present note is to understand whether it is possible to define interacting quantum field theory in global anti de Sitter space-time with Lorentzian signature, in its covering space-time (whose time coordinate is not periodic) and in its Poincare patch. We show that in global anti de Sitter space-time there are certain problems to define 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 space-time. At the same time quantum field theory in Poincare region of the AdS space-time 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 space-time. However, to do that one has to use an unusual $i\epsilon$-prescription in the Feynman propagator, which cannot be used in loop calculations in non-stationary situations.