Comments on the scalar propagator in AdS x S and the BMN plane wave

TL;DR

This paper analyzes scalar propagators in AdS x S backgrounds, highlighting their dependence on geometric distances, and relates these to the BMN plane wave limit, providing new insights into their structure and interpretation.

Contribution

It provides a detailed analysis of scalar propagators in AdS x S spaces, including conformally flat cases and their relation to the BMN plane wave limit, with a geometric interpretation.

Findings

Propagators are powerlike in chordal distances for conformally flat cases.

In general cases, propagators depend on both chordal distances separately.

Relation established between AdS x S propagators and BMN plane wave expressions.

Abstract

We discuss the scalar propagator on generic AdS_{d+1} x S^{d'+1} backgrounds. For the conformally flat situations and masses corresponding to Weyl invariant actions the propagator is powerlike in the sum of the chordal distances with respect to AdS_{d+1} and S^{d'+1}. In all other cases the propagator depends on both chordal distances separately. We discuss the KK mode summation to construct the propagator in brief. For AdS_5 x S^5 we relate our propagator to the expression in the BMN plane wave limit and find a geometric interpretation of the variables occurring in the known explicit construction on the plane wave.