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

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.