Background independence of effective actions at critical dimension

Recently, by explicit calculations at orders $\alpha',\alpha'^2,\alpha'^3$, it has been observed that the effective action of string theory critical dimension is independent background for closed spacetime manifolds. In this paper we speculate open manifolds, even character boundary, \ie boundary couplings timelike and spacelike boundaries are same. We support proposal calculating in bosonic order $\alpha'$ show they same as have recently found.