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 is shown to induce compatible Batalin--Fradkin--Vilkovisky data, thus allowing BV-quantisation manifolds boundary. On the other hand, analogous formulation of Nambu--Goto fails satisfy needed regularity requirements. As byproduct, concise description given reduced phase spaces both models and their relation, any target $d$-dimensional Lorentzian manifold.