BV analysis of Polyakov and Nambu-Goto theories with boundary

The Batalin-Vilkovisky data for Polyakov string theory on a manifold with (non-null) boundary are shown to induce compatible Batalin-Fradkin-Vilkovisky data, thus allowing BV-quantisation on manifolds with boundary. On the other hand, the analogous formulation of Nambu-Goto string theory fails to satisfy the needed regularity requirements. As a by-product, a concise description is given of the reduced phase spaces of both models and their relation, for any target d-dimensional Lorentzian manifold.