  I present lattice Monte Carlo calculations for a universal four-component
Fermi gas confined to a finite box and to a harmonic trap in one spatial
dimension. I obtain the values xi_1d = 0.370(4) and xi_1d = 0.372(1),
respectively, for the Bertsch parameter, a nonperturbative universal constant
defined as the (square of the) energy of the untrapped (trapped) system
measured in units of the free gas energy. The Bertsch parameter for the
one-dimensional system is consistent to within ~1% uncertainties with the most
recent numerical and experimental estimates of the analogous Bertsch parameter
for a three-dimensional spin-1/2 Fermi gas at unitarity. The finding suggests
the intriguing possibility that there exists a universality between two
conformal theories in different dimensions. To lend support to this study, I
also compute continuum extrapolated ground state energies for four and five
fermions confined to a harmonic trap and demonstrate the restoration of a
Virial theorem in the continuum limit. The continuum few-body energies obtained
are consistent with exact analytical calculations to within ~1.0% and ~0.25%
statistical uncertainties, respectively.
