Bosonic string theories with new boundary conditions

Abstract

We show that the classical Nambu-Goto string in D dimensions admits Poincaré invariance ind dimensions (d≤D) if (i)d-2 of the transverse co-ordinates xⁱ are periodic and the rest quasi-periodic involving a real orthogonal matrix with (D−d) (D−d−1)/2 free parameters, or if (ii) d−2 of xⁱ obey Neumann and the rest obey a boundary condition involving N free parameters, where N=(D−d)²/2 if D−d is even, and N=[(D-d)²−1]/2 if D−d is odd.