The motivic Galois action conjecture for free massless field theories

Let $\mathfrak{g}^*$ be the homotopy Lie algebra associated with the free massless theory in dimension $d$, and let $G_{M,\mathrm{Betti}}$ be the motivic Galois group in the Betti realization. Let $GT$ denote the Grothendieck-Teichmüller group. The motivic Galois action conjecture for free massless theories. The motivic Galois group $G_{M,\mathrm{Betti}}$ acts, in the homotopy sense, on $\mathfrak{g}^*$ in every dimension; in even dimension this action factors through $GT$, and it should be related to the action on values of Feynman integrals. The source gives this as a conjectural expectation and no resolution status.