Event-chain Monte Carlo (ECMC) accelerates the sampling of hard-sphere systems, and has been generalized to the potentials used in classical molecular simulation. Rather than imposing detailed balance on transition probabilities, the method enforces a weaker global-balance condition in order to guarantee convergence to equilibrium. In this paper we generalize the factor-field variant of ECMC to higher space dimensions. In the two-dimensional fluid phase, factor-field ECMC saturates the lower bound $z=0$ for the dynamical scaling exponent for local dynamics, whereas molecular dynamics is characterized by $z=1$ and local Metropolis Monte Carlo by $z=2$. In the presence of hexatic order, factor fields are not found to speed up the convergence. We indicate applications to the physics of glasses, and note that generalizations of factor fields could couple to orientational order.