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

• Published in: Nuclear physics. B Vol. 578; no. 3; pp. 552 - 576
• Main Author: Saleur, H.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 10.07.2000
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/S0550-3213(00)00002-X

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.