Efimov-like physics in fraction-dimensional Bose systems with three-body interaction

A few-body properties of spinless Bose particles interacting via the contact three-body potential in geometries with fractional dimensions $1<d<2$ are considered. In the four-body sector at three-body resonance we predict the existence of infinite tower of the Efimov bound states, and a similar behavior is found in the five-body problem. It is shown that a ratio of the high-energy levels in these two sectors is a universal constant. The consequences of emergence of the Efimov physics on the many-body behavior are briefly discussed.