Effective super Tonks-Girardeau gases as ground states of strongly attractive multi-component fermions

In the strong interaction limit, attractive fermions with $N$-component hyperfine states in a one-dimensional waveguide form unbreakable bound cluster states. We demonstrate that the ground state of strongly attractive SU($N$) Fermi gases can be effectively described by a super Tonks-Girardeau gas-like state composed of bosonic cluster states with strongly attractive cluster-cluster interaction for even $N$, and a Fermi duality of a super Tonks-Girardeau gas-like state composed of fermionic cluster states with weakly interacting cluster-cluster p-wave interaction for odd $N$.