Comment on thickness corrections to the Nambu wall

Abstract We comment on some calculations concerning the finite-thickness corrections to the (generalized) Nambu action for a curved domain wall in Minkowski space. Contrary to a recent claim in the literature, we find no first order corrections in the wall thickness, and only one second order correction proportional to the Ricci curvature of the wall. These results are obtained by consistently expanding the action and the equations of motion for the scalar field.