Characterization of metric spaces whose free space is isometric to ${\mathrm{\ell }}_1$

We characterize metric spaces whose Lipschitz free space is isometric to ${\mathrm{\ell }}_1$. In particular, the Lipschitz free space over an ultrametric space is not isometric to ${\mathrm{\ell }}_1(\mathrm{\Gamma })$ for any set $\mathrm{\Gamma }$. We give a lower bound for the Banach-Mazur distance in the finite case.