 Little group with mixed string boundary conditions

The symmetry used to classify an open string must preserve its endpoint boundary background as well as its momentum. A Neumann-Dirichlet open-string boundary condition breaks target Lorentz transformations mixing ND and common directions with Neumann boundary conditions. For a D1–D25 pair with 24 ND directions, the common worldvolume has Lorentz group $SO(1,1)$, whose connected massive little group is trivial. The transverse $SO(24)$ remains as an internal rotation group. Thus a massive 24-component oscillator multiplet is not an $SO(25)$ vector of the full 26-dimensional massive little group; a vector of that full group would have 25 components.