On the Kählerian symmetries of the two-loop action of the effective string theory

Sometimes ago, it has been proposed in a paper by N.Kaloper and K.A.Meissner (\PR {\bf D56} (1997) 7940) that if one makes local redefinitions of fields, it does not change the equations of motion (in the redefined fields); however, this comment has not generally been accepted, namely, the redefined fields satisfy different equations of motion. For this reason, in this paper, it is proved that the whole action can be written as a square of the zeroth-order field equations. In this way, we show that any solution of the zeroth-order field equations, which has some K\"{a}hler symmetry, at the same time, is also a solution of the two-loop equations.