The boundary beta-function generates the renormalization group acting on
the universality classes of one-dimensional quantum systems with boundary
which are critical in the bulk but not critical at the boundary. In 1991
I. Affleck and A. Ludwig put forward a conjecture usually refered to as
the "g-theorem" that is a statement about general behavior of
boundary flows analogous to Zamolodchikov's c-theorem in the bulk.
I will present a proof of their conjecture from first principles found by
Daniel Friedan and myself in hep-th/0312197. Relation with boundary string
field theory will be discussed.