  Recently it has been proposed that the consistency with T-duality requires
the effective action of string theory at order $\alpha'^n$ satisfies the least
action principle provided that the values of the massless fields and their
derivatives up to order $n$ are known on the boundary. In this paper we
speculate that this boundary condition constrains the field redefinitions and
the corrections to the T-duality transformations in the presence of boundary,
\eg at order $\alpha'$, the metric does not change, and all other massless
fields should change to include only the first derivative of the massless
fields.
  Using the above field redefinitions, we write all gauge invariant bulk and
boundary couplings in the bosonic string theory at order $\alpha'$ in a minimal
scheme. Then using the assumption that the classical effective action of the
string theory at the critical dimension is background independent, we fix the
coefficients of the independent gauge invariant couplings by imposing $O(1,1)$
symmetry when the background has a circle and by imposing $O(d,d)$ symmetry
when the background has $T^d$. These constraints fix the bulk action up to an
overall factor, and the boundary action up to two parameters. By requiring the
gravity couplings in the boundary action to be consistent with those in the
Chern-Simons gravity, the two boundary parameters are also fixed. Up to the
above restricted field redefinitions, the bulk and boundary couplings are
exactly those in the K.A. Meissner action and its corresponding boundary
action.
