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.
Highlights
Classical and quantum field theory in anti–de Sitter (AdS) space is quite well developed: see [1,2] for reviews and, e.g., [3,4,5] for the approach close to the one adopted in the present paper
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
Loop corrections in Lorentzian AdS space have some peculiarities [13] related to the presence of additional UV singularities in the propagators, which are sitting on the light cone emanating from the antipodal point of the source
Summary
Classical and quantum field theory in anti–de Sitter (AdS) space is quite well developed: see [1,2] for reviews and, e.g., [3,4,5] for the approach close to the one adopted in the present paper. Loop corrections in Lorentzian AdS space have some peculiarities [13] related to the presence of additional UV singularities in the propagators, which are sitting on the light cone emanating from the antipodal point of the source. Such singularities are not present in flat spacetime or in EAdS. The goal of the present paper is to understand whether it is possible to define interacting quantum field theory in global AdS spacetime with Lorentzian signature, in its covering spacetime (CAdS) and in its Poincarepatch (PP). To make the paper self-contained we provide some technical details in the Appendixes
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