Abstract :
I discuss in this paper the continuum limit of integrable spin chains based on the superalgebras sl(N/K) . The general conclusion is that, with the full “supersymmetry”, none of these models is relativistic. When the supersymmetry is broken by the generator of the sub u(1) , Gross–Neveu models of various types are obtained. For instance, in the case of sl(N/K) with a typical fermionic representation on every site, the continuum limit is the GN model with N colors and K flavors. In the case of sl(N/1) and atypical representations of spin j , a close cousin of the GN model with N colors and j flavors with flavor anisotropy is obtained. The Dynkin parameter associated with the fermionic root, while providing solutions of the Yang–Baxter equation with a continuous parameter, thus does not give rise to any new physics in the field theory limit.
