  We construct quantum effective action in spacetimes with branes (boundaries)
and establish its relation to the "cosmological wave function" of the bulk --
the solution of the corresponding Wheeler-DeWitt equation which can be
considered as a means of the holographic description of braneworld models. We
show that for a special type of the bulk-brane gauge fixing procedure the
one-loop part of the action decouples into the additive sum of brane-to-brane
and bulk-to-bulk effective actions, and this decomposition proliferates in a
special way in higher orders of the Feynman diagrammatic expansion. This
property is based on a special duality relation between the Dirichlet and
Neumann boundary value problems when applied to the functional determinants of
wave operators and the field-theoretic version of the well-known semiclassical
Van Vleck-Morette determinant. It facilitates the gauge-independent way of
treating the strong-coupling and VDVZ problems in brane induced gravity models.
Importance of this technique in various implications of braneworld theory and
infrared modifications of Einstein theory is briefly discussed.
