  We study the consequences of the presence of a boundary in topological field
theories in various dimensions. We characterize, univocally and on very general
grounds, the field content and the symmetries of the actions which live on the
boundary. We then show that these actions are covariant, despite appearances.
We show also that physically relevant theories like the 2D Luttinger liquid
model, or the 4D Maxwell theory, can be seen as boundary reductions of higher
dimensional topological field theories, which do not display local observables.
