Antisymmetric string actions

An action is presented for the free bosonic string on external flat space in terms of an antisymmetric second-rank string background tensor which is classically equivalent to the Nambu-Goto action. Both action and field equations are entirely described in terms of 2D world-sheet forms, without any reference to a 2D metric tensor background. The analysis of its canonical formulation shows how the quadratic Virasoro constraints are generated in this case and what their connection with the Bianchi identities are. Since in the orthonormal gauge the reduced action coincides with the standard one, it has the same critical dimension D=26. The existence of an interaction term of a purely geometric structure stemming in the extrinsic curvature is pointed out. Its action and the new string field equations are then derived. This polynomial anti-symmetric string action is uniformly generalized in order to describe d<D-dimensional extended objects in D-dimensional flat space. (orig.)