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

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