A Solvable Sector of AdS Theory
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_\pm = (d\pm 1)/2 in AdS_{d+1} the corresponding effective conformal theory has propagators |\vec p |^{-1} and vertices (|\vec p_1| + ... + |\vec p_n|)^{-s_n} of valence n in momentum representation, with s_n = (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.