  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 \Delta_\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)\Delta_- - 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.
