A large class of two-dimensional quantum fields theories contain an interesting operator built from the stress tensor, called "TTbar". Although this operator is irrelevant, adding it to the action generates a new family of theories in a controlled way. For conformal field theories with an Anti-de Sitter holographic dual, it has been conjectured that the TTbar deformation corresponds to "cutting off" the region of AdS beyond a hypersurface of fixed radius. We use the variational principle in the CFT to derive the holographic effect of the TTbar deformation at large N: it changes the boundary conditions of the metric at infinity. In the absence of matter and for a particular sign of the deformation parameter, this can be reinterpreted as Dirichlet conditions at finite radius; albeit without discarding the region outside. This interpretation breaks down when matter is present, whereas the mixed boundary conditions prevail. The asymptotic symmetries of the gravitational theory with mixed boundary conditions form two Virasoro algebras, the generators of which are state-dependent but the central charge remains unchanged.
