Exactly solvable model for isospin S=3/2 fermionic atoms on an optical lattice

We propose an exact solution of a model describing a low energy behavior of cold isospin S=3/2 fermionic atoms on a one-dimensional optical lattice. Depending on the band filling the effective field theory has a form of a deformed Gross-Neveu model with either O(7)xZ(2) (half filling) or U(1)xO(5)xZ(2) symmetry.