A Solvable Sector of AdS Theory

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Field theory in space-time with boundary has an interesting sub-sector, where propagator is difference of those with Neumann and Dirichlet boundary conditions. Such boundary-induced theory in the bulk is essentially holomorphic and is exactly solvable in the sense that all orders of perturbation theory can be summed up explicitly into effective non-local theory at the boundary. This provides a non-trivial realization of holography principle. In the particular example of scalar fields of dimensions Δ± = (d± 1)/2 in AdSd₊₁ the corresponding effective conformal theory has propagators | p |⁻¹ and vertices (| p₁| +... + | pₙ|)⁻ˢⁿ of valence n in momentum representation, with sₙ = (n-2)Δ- - 1. This extraordinary simplicity of certain amplitudes in AdS seems inspiring and can be helpful for analyzing corollaries of open-closed string duality for particular field-theory sub-sectors of string theory.