Article

# Scalar propagator in the pp-wave geometry obtained from AdS5×S5

Department of Physics, The Ohio State University, Columbus, OH 43210, USA

Nuclear Physics B (Impact Factor: 3.95). 09/2002; DOI: 10.1016/S0550-3213(02)00568-0 Source: arXiv

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**ABSTRACT:**We discuss the scalar propagator on generic AdSd+1 × Sd '+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 AdSd+1 and Sd '+1. In these cases we analyze its source structure. In all other cases the propagator depends on both chordal distances separately. There an explicit formula is found for certain special mass values. For pure AdS we show how the well known propagators in the Weyl invariant case can be expressed as linear combinations of simple powers of the chordal distance. For AdS5 × S5 we relate our propagator to the expression in the plane wave limit and find a geometric interpretation of the variables occurring in the known explicit construction on the plane wave. As a byproduct of comparing different techniques, including the KK mode summation, a theorem for summing certain products of Legendre and Gegenbauer functions is derived.Journal of High Energy Physics 02/2005; 2(02):047-047. · 6.22 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Green functions for the scalar, spinor and vector fields in a plane wave geometry arising as a Penrose limit of AdS × 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 × S with equal radii, and for a number of other illustrative cases.Journal of High Energy Physics 08/2004; 8(08):008-008. · 6.22 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We discuss the scalar propagator on generic ADSd+1 × Sd+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 AdSd+1 and Sd+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 AdS5 × S5 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.Fortschritte der Physik 06/2004; 52(67):684-689. · 0.98 Impact Factor

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