Propagators and WKB-exactness in the plane wave limit of AdSxS

TL;DR

This paper derives exact propagators for scalar, spinor, and vector fields in a plane wave limit of AdS×S, revealing WKB-exactness and structural similarities to flat space, with implications for quantum field theory in curved backgrounds.

Contribution

It demonstrates that the Schwinger-DeWitt technique yields WKB-exact propagators in the plane wave limit of AdS×S, and shows how to obtain these propagators using the first geodesic terms, simplifying calculations.

Findings

Propagators are WKB-exact in the plane wave background.

Structural similarity between plane wave and flat space propagators is established.

First geodesic terms suffice for correct propagators in the Penrose limit.

Abstract

Green functions for the scalar, spinor and vector fields in a plane wave geometry arising as a Penrose limit of $AdS\times S$ are obtained. The Schwinger-DeWitt technique directly gives the results in the plane wave background, which turns out to be WKB-exact. Therefore the structural similarity with flat space results is unveiled. In addition, based on the local character of the Penrose limit, it is claimed that for getting the correct propagators in the limit one can rely on the first terms of the direct geodesic contribution in the Schwinger-DeWitt expansion of the original propagators . This is explicitly shown for the Einstein Static Universe, which has the same Penrose limit as $AdS\times S$ with equal radii, and for a number of other illustrative cases.