On the propagator of a scalar field in AdS x S and in its plane wave limit

Abstract

We discuss the scalar propagator on generic AdS x S 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 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 AdS(5) x S(5) 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.

26 pages, LaTeX, 1 figure; extended final version, section added

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• String amplitudes in the Hpp-wave limit of AdS3xS3
• AdS/CFT in superspace
• Properties of branes in curved spacetimes
• Bulk reconstruction of metrics with a compact space asymptotically
• Gravitino Propagator in anti de Sitter space
• Oscillator quantization of the massive scalar particle dynamics on AdS spacetime
• Massless scalar particle on AdS spacetime: Hamiltonian reduction and quantization
• Quantization of AdS x S particle in static gauge
• Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
• Configuration Space Methods and Time Ordering for Scalar Propagators in (Anti and) de Sitter Spacetimes
• Spacecone quantization of AdS superparticle
• Local Commutativity and Causality in Interacting PP-wave String Field Theory
• The Transition Amplitude for 2T Physics
• Propagators and WKB-exactness in the plane wave limit of AdSxS