Bosonic string theories with new boundary conditions

Abstract

We show that the classical Nambu-Goto string inD dimensions admits Poincaré invariance ind dimensions (d⩽D) if (i)d − 2 of the transverse co-ordinatesx ⁱ 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 ofx ⁱ obey Neumann and the rest obey a boundary condition involvingN free parameters, whereN=(D − d)²/2 ifD − d is even, andN=[(D − d)² − 1]/2 ifD − d is odd.