Abstract
In this paper, we calculate higher point tree level vector amplitudes propagating in AdS4, or equivalently the dual boundary current correlators. We use bulk perturbation theory to compute tree level Witten diagrams. We show that when these amplitudes are written in momentum space, they reduce to relatively simple expressions. We explicitly compute four and five point correlators and also sketch a general strategy to compute the full six-point correlators.
Highlights
We show that when these amplitudes are written in momentum space, they reduce to relatively simple expressions
The resultant scattering amplitudes in AdS space are related to CFT correlation functions
With the AdS/CFT correspondence, correlation functions can be computed by perturbative calculations that can be diagrammatically represented by Witten diagrams
Summary
The main emphasis of this section is to quickly review the perturbation theory in Anti-de Sitter space. External lines which connect the bulk point of the AdS to the boundary, 2. Internal lines that propagate the fields, 3. One can find the bulk to bulk propagators (which we will denote as BtB ) by solving the Green’s function. By taking one of the points to the boundary, we can obtain the external lines, i.e. the bulk-to-boundary propagators (which we will denote as Btb ) where they correspond to propagation of some field perturbation into the bulk. One integrates over the bulk interaction points, denoted as z below. We will first discuss the propagators and list possible solutions as equations of motion both for scalars and vectors in AdS. We will use them in the simplest Witten diagram: a three point amplitude
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