On the Local Frame in Nonlinear Higher-Spin Equations

Properties of the resolution operator ${\rm d}_{loc}^*$ in higher-spin equations, that leads to local current interactions at the cubic order and minimally nonlocal higher-order corrections, are formulated in terms of the condition on the class of master fields of higher-spin theory that restricts both the dependence on the spinor $Y$, $Z$ variables and on the contractions of indices between the constituent fields in bilinear terms. The Green function in the sector of zero-forms is found for the case of constituent fields carrying helicities of opposite signs. It is shown that the local resolution ${\rm d}_{loc}^*$ differs from the conventional De Rham resolution ${\rm d}_Z^*$ by a non-local shift.