Holographic relation between $p$-adic effective action and string field theory

We consider two holographically related theories. As the first $(d+1)$-dimensional theory, we consider a model in which the $(d+1)$-dimensional space is the direct product of $\mathbb R^d$ and the half-axis $\mathbb R_+$ and in which the kinetic operator has a nonlocal term induced by the nonlocal kinetic operator of the $p$-adic effective action. It turns out that the kinetic operator in the second, holographically related, $d$-dimensional theory is the kinetic operator of the string field theory effective action.