  We present quantum Monte Carlo calculations of light nuclei, neutron-$\alpha$
scattering, and neutron matter using local two- and three-nucleon ($3N$)
interactions derived from chiral effective field theory up to
next-to-next-to-leading order (N$^2$LO). The two undetermined $3N$ low-energy
couplings are fit to the $^4$He binding energy and, for the first time, to the
spin-orbit splitting in the neutron-$\alpha$ $P$-wave phase shifts.
Furthermore, we investigate different choices of local $3N$-operator structures
and find that chiral interactions at N$^2$LO are able to simultaneously
reproduce the properties of $A=3,4,5$ systems and of neutron matter, in
contrast to commonly used phenomenological $3N$ interactions.

Nuclear Theory;Nuclear Experiment