The continuum limit of sl(N/K) integrable super spin chains

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. These features generalize to the case where an impurity is embedded in the system. (C) 2000 Elsevier Science B.V. All rights reserved.