  We show that a system of three species of one-dimensional fermions, with an
attractive three-body contact interaction, features a scale anomaly directly
related to the anomaly of two-dimensional fermions with two-body forces. We
show, furthermore, that those two cases (and their multi species
generalizations) are the only non-relativistic systems with contact
interactions that display a scale anomaly. While the two-dimensional case is
well-known and has been under study both experimentally and theoretically for
years, the one-dimensional case presented here has remained unexplored. For the
latter, we calculate the impact of the anomaly on the equation of state, which
appears through the generalization of Tan's contact for three-body forces, and
determine the pressure at finite temperature. In addition, we show that the
third-order virial coefficient is proportional to the second-order coefficient
of the two-dimensional two-body case.
