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It was shown [Chin. Phys. Lett. 28, 020503 (2011)] that at zero temperaturethe ground state of the one-dimensional (1D) $w$-component Fermi gas coincideswith that of the spinless Bose gas in the limit $\omega\to \infty$. Thisbehaviour was experimentally evidenced through a quasi-1D tightly trappingultracold ${}^{173}$Yb atoms in the recent paper [Nature Physics 10, 198(2014)]. However, understanding of low temperature behaviour of the Fermi gaseswith a repulsive interaction acquires spin-charge separated conformal fieldtheories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic$SU(w)$ Heisenberg spin chain. Here we analytically derive universalthermodynamics of 1D strongly repulsive fermionic gases with $SU(w)$ symmetryvia the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energyand magnetic properties of the systems at low temperatures in a weak magneticfield are obtained through the Wiener-Hopf method. In particular, the freeenergy essentially manifests the spin-charge separated conformal field theoriesfor the high symmetry systems with arbitrary repulsive interaction strength. Wealso find that the sound velocity of the Fermi gases in the large $w$ limitcoincides with that for the spinless Bose gas, whereas the spin velocityvanishes quickly as $w$ becomes large. This indicates a strong suppression ofthe Fermi exclusion statistics by the commutativity feature among the$w$-component fermions with different spin states in the Tomonaga-Luttingerliquid phase. Moreover, the equations of state and critical behaviour ofphysical quantities at finite temperatures are analytically derived in terms ofthe polylogarithm functions in the quantum critical region.

Universal low energy physics in one-dimensional multicompnent Fermi gases with a strongly repulsive $\delta$-function interaction